diff --git a/src/bicgstab.jl b/src/bicgstab.jl
index 269317102..ab09098bf 100644
--- a/src/bicgstab.jl
+++ b/src/bicgstab.jl
@@ -62,17 +62,17 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `c`:
-* `M`:
-* `N`:
-* `ldiv`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `c`: the second initial vector of length `n` required by the Lanczos biorthogonalization process;
+* `M`: linear operator that models a nonsingular matrix of size `n` used for left preconditioning;
+* `N`: linear operator that models a nonsingular matrix of size `n` used for right preconditioning;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/bilq.jl b/src/bilq.jl
index d7110408c..aa1766217 100644
--- a/src/bilq.jl
+++ b/src/bilq.jl
@@ -48,15 +48,15 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `c`:
-* `transfer_to_bicg`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `c`: the second initial vector of length `n` required by the Lanczos biorthogonalization process;
+* `transfer_to_bicg`: transfer from the BiLQ point to the BiCG point, when it exists. The transfer is based on the residual norm;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/bilqr.jl b/src/bilqr.jl
index 07641ff90..0d6e2d168 100644
--- a/src/bilqr.jl
+++ b/src/bilqr.jl
@@ -54,14 +54,14 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `transfer_to_bicg`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `transfer_to_bicg`: transfer from the BiLQ point to the BiCG point, when it exists. The transfer is based on the residual norm;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/cg.jl b/src/cg.jl
index 4042488a2..cf155561a 100644
--- a/src/cg.jl
+++ b/src/cg.jl
@@ -54,17 +54,17 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `radius`:
-* `linesearch`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `radius`: add the trust-region constraint ‖x‖ ≤ `radius` if `radius > 0`. Useful to compute a step in a trust-region method for optimization;
+* `linesearch`: if `true`, indicate that the solution is to be used in an inexact Newton method with linesearch. If negative curvature is detected at iteration k > 0, the solution of iteration k-1 is returned. If negative curvature is detected at iteration 0, the right-hand side is returned (i.e., the negative gradient);
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/cg_lanczos.jl b/src/cg_lanczos.jl
index f09a4ca29..eac44e11d 100644
--- a/src/cg_lanczos.jl
+++ b/src/cg_lanczos.jl
@@ -49,16 +49,16 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `check_curvature`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `check_curvature`: if `true`, check that the curvature of the quadratic along the search direction is positive, and abort if not, unless `linesearch` is also `true`;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/cg_lanczos_shift.jl b/src/cg_lanczos_shift.jl
index a647b9114..5b9833484 100644
--- a/src/cg_lanczos_shift.jl
+++ b/src/cg_lanczos_shift.jl
@@ -45,16 +45,16 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `check_curvature`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `check_curvature`: if `true`, check that the curvature of the quadratic along the search direction is positive, and abort if not, unless `linesearch` is also `true`;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/cgls.jl b/src/cgls.jl
index ebf54ace1..5fe6449cb 100644
--- a/src/cgls.jl
+++ b/src/cgls.jl
@@ -63,17 +63,17 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `radius`:
-* `λ`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `radius`: add the trust-region constraint ‖x‖ ≤ `radius` if `radius > 0`. Useful to compute a step in a trust-region method for optimization;
+* `λ`: regularization parameter;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/cgne.jl b/src/cgne.jl
index 2750d2a5f..e4aff6ddf 100644
--- a/src/cgne.jl
+++ b/src/cgne.jl
@@ -74,15 +74,15 @@ and `false` otherwise.
 #### Keyword arguments
 
 * `N`:
-* `ldiv`:
-* `λ`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `λ`: regularization parameter;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/cgs.jl b/src/cgs.jl
index 2f166c4ce..336f80e10 100644
--- a/src/cgs.jl
+++ b/src/cgs.jl
@@ -60,17 +60,17 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `c`:
-* `M`:
-* `N`:
-* `ldiv`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `c`: the second initial vector of length `n` required by the Lanczos biorthogonalization process;
+* `M`: linear operator that models a nonsingular matrix of size `n` used for left preconditioning;
+* `N`: linear operator that models a nonsingular matrix of size `n` used for right preconditioning;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/cr.jl b/src/cr.jl
index 415c10a3a..83e1bc10e 100644
--- a/src/cr.jl
+++ b/src/cr.jl
@@ -54,18 +54,18 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `radius`:
-* `linesearch`:
-* `γ`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `radius`: add the trust-region constraint ‖x‖ ≤ `radius` if `radius > 0`. Useful to compute a step in a trust-region method for optimization;
+* `linesearch`: if `true`, indicate that the solution is to be used in an inexact Newton method with linesearch. If negative curvature is detected at iteration k > 0, the solution of iteration k-1 is returned. If negative curvature is detected at iteration 0, the right-hand side is returned (i.e., the negative gradient);
+* `γ`: tolerance to determine that the curvature of the quadratic model is nonpositive;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/craig.jl b/src/craig.jl
index 443c26570..72b803724 100644
--- a/src/craig.jl
+++ b/src/craig.jl
@@ -98,21 +98,21 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `N`:
-* `ldiv`:
-* `transfer_to_lsqr`:
-* `sqd`:
-* `λ`:
-* `btol`:
-* `conlim`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `m` used for centered preconditioning of the augmented system;
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning of the augmented system;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `transfer_to_lsqr`: transfer from the LSLQ point to the LSQR point, when it exists. The transfer is based on the residual norm;
+* `sqd`: if `true`, set `λ=1` for Hermitian quasi-definite systems;
+* `λ`: regularization parameter;
+* `btol`: stopping tolerance used to detect zero-residual problems;
+* `conlim`: limit on the estimated condition number of `A` beyond which the solution will be abandoned;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/craigmr.jl b/src/craigmr.jl
index 66ec8a360..ce5087de7 100644
--- a/src/craigmr.jl
+++ b/src/craigmr.jl
@@ -93,18 +93,18 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `N`:
-* `ldiv`:
-* `sqd`:
-* `λ`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `m` used for centered preconditioning of the augmented system;
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning of the augmented system;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `sqd`: if `true`, set `λ=1` for Hermitian quasi-definite systems;
+* `λ`: regularization parameter;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/crls.jl b/src/crls.jl
index 2ce904edf..cc98fb1be 100644
--- a/src/crls.jl
+++ b/src/crls.jl
@@ -55,17 +55,17 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `radius`:
-* `λ`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `radius`: add the trust-region constraint ‖x‖ ≤ `radius` if `radius > 0`. Useful to compute a step in a trust-region method for optimization;
+* `λ`: regularization parameter;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/crmr.jl b/src/crmr.jl
index e9dd9a675..bd4fd81f0 100644
--- a/src/crmr.jl
+++ b/src/crmr.jl
@@ -72,15 +72,15 @@ and `false` otherwise.
 #### Keyword arguments
 
 * `N`:
-* `ldiv`:
-* `λ`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `λ`: regularization parameter;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/diom.jl b/src/diom.jl
index f745e17f1..9c61e513b 100644
--- a/src/diom.jl
+++ b/src/diom.jl
@@ -53,18 +53,18 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `memory`:
-* `M`:
-* `N`:
-* `ldiv`:
-* `reorthogonalization`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `memory`: the number of most recent vectors of the Krylov basis against which to orthogonalize a new vector;
+* `M`: linear operator that models a nonsingular matrix of size `n` used for left preconditioning;
+* `N`: linear operator that models a nonsingular matrix of size `n` used for right preconditioning;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `reorthogonalization`: reorthogonalize the new vectors of the Krylov basis against the `memory` most recent vectors;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/dqgmres.jl b/src/dqgmres.jl
index f2efbf391..d0fe6ffaf 100644
--- a/src/dqgmres.jl
+++ b/src/dqgmres.jl
@@ -53,18 +53,18 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `memory`:
-* `M`:
-* `N`:
-* `reorthogonalization`:
-* `ldiv`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `memory`: the number of most recent vectors of the Krylov basis against which to orthogonalize a new vector;
+* `M`: linear operator that models a nonsingular matrix of size `n` used for left preconditioning;
+* `N`: linear operator that models a nonsingular matrix of size `n` used for right preconditioning;
+* `reorthogonalization`: reorthogonalize the new vectors of the Krylov basis against the `memory` most recent vectors;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/fgmres.jl b/src/fgmres.jl
index b00c24d04..b25131736 100644
--- a/src/fgmres.jl
+++ b/src/fgmres.jl
@@ -56,19 +56,19 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `memory`:
-* `M`:
-* `N`:
-* `ldiv`:
-* `restart`:
-* `reorthogonalization`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `memory`: if `restart = true`, the restarted version FGMRES(k) is used with `k = memory`. If `restart = false`, the parameter `memory` should be used as a hint of the number of iterations to limit dynamic memory allocations. Additional storage will be allocated if the number of iterations exceeds `memory`;
+* `M`: linear operator that models a nonsingular matrix of size `n` used for left preconditioning;
+* `N`: linear operator that models a nonsingular matrix of size `n` used for right preconditioning;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `restart`: restart the method after `memory` iterations;
+* `reorthogonalization`: reorthogonalize the new vectors of the Krylov basis against all previous vectors;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/fom.jl b/src/fom.jl
index 177c02d3d..b6d057998 100644
--- a/src/fom.jl
+++ b/src/fom.jl
@@ -50,19 +50,19 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `memory`:
-* `M`:
-* `N`:
-* `ldiv`:
-* `restart`:
-* `reorthogonalization`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `memory`: if `restart = true`, the restarted version FOM(k) is used with `k = memory`. If `restart = false`, the parameter `memory` should be used as a hint of the number of iterations to limit dynamic memory allocations. Additional storage will be allocated if the number of iterations exceeds `memory`;
+* `M`: linear operator that models a nonsingular matrix of size `n` used for left preconditioning;
+* `N`: linear operator that models a nonsingular matrix of size `n` used for right preconditioning;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `restart`: restart the method after `memory` iterations;
+* `reorthogonalization`: reorthogonalize the new vectors of the Krylov basis against all previous vectors;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/gmres.jl b/src/gmres.jl
index 8d66f23cd..4a238f2a6 100644
--- a/src/gmres.jl
+++ b/src/gmres.jl
@@ -50,19 +50,19 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `memory`:
-* `M`:
-* `N`:
-* `ldiv`:
-* `restart`:
-* `reorthogonalization`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `memory`: if `restart = true`, the restarted version GMRES(k) is used with `k = memory`. If `restart = false`, the parameter `memory` should be used as a hint of the number of iterations to limit dynamic memory allocations. Additional storage will be allocated if the number of iterations exceeds `memory`;
+* `M`: linear operator that models a nonsingular matrix of size `n` used for left preconditioning;
+* `N`: linear operator that models a nonsingular matrix of size `n` used for right preconditioning;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `restart`: restart the method after `memory` iterations;
+* `reorthogonalization`: reorthogonalize the new vectors of the Krylov basis against all previous vectors;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/gpmr.jl b/src/gpmr.jl
index 94db27476..75cbcac26 100644
--- a/src/gpmr.jl
+++ b/src/gpmr.jl
@@ -82,22 +82,22 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `memory`:
-* `C`:
-* `D`:
-* `E`:
-* `F`:
-* `ldiv`:
-* `gsp`:
-* `λ` and `μ`:
-* `reorthogonalization`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `memory`: if `restart = true`, the restarted version GPMR(k) is used with `k = memory`. If `restart = false`, the parameter `memory` should be used as a hint of the number of iterations to limit dynamic memory allocations. Additional storage will be allocated if the number of iterations exceeds `memory`;
+* `C`: linear operator that models a nonsingular matrix of size `m`, and represents the first term of the block-diagonal left preconditioner;
+* `D`: linear operator that models a nonsingular matrix of size `n`, and represents the second term of the block-diagonal left preconditioner;
+* `E`: linear operator that models a nonsingular matrix of size `m`, and represents the first term of the block-diagonal right preconditioner;
+* `F`: linear operator that models a nonsingular matrix of size `n`, and represents the second term of the block-diagonal right preconditioner;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `gsp`: if `true`, set `λ = 1` and `μ = 0` for generalized saddle-point systems;
+* `λ` and `μ`: diagonal scaling factors of the partitioned linear system;
+* `reorthogonalization`: reorthogonalize the new vectors of the Krylov basis against all previous vectors;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/lnlq.jl b/src/lnlq.jl
index e231cc6ee..e2d4f89bc 100644
--- a/src/lnlq.jl
+++ b/src/lnlq.jl
@@ -93,22 +93,22 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `N`:
-* `ldiv`:
-* `transfer_to_craig`:
-* `sqd`:
-* `λ`:
-* `σ`:
-* `utolx`:
-* `utoly`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `m` used for centered preconditioning of the augmented system;
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning of the augmented system;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `transfer_to_craig`: transfer from the LNLQ point to the CRAIG point, when it exists. The transfer is based on the residual norm;
+* `sqd`: if `true`, set `λ=1` for Hermitian quasi-definite systems;
+* `λ`: regularization parameter;
+* `σ`: strict lower bound on the smallest positive singular value `σₘᵢₙ` such as `σ = (1-10⁻⁷)σₘᵢₙ`;
+* `utolx`: tolerance on the upper bound on the distance to the solution `‖x-x*‖`;
+* `utoly`: tolerance on the upper bound on the distance to the solution `‖y-y*‖`;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/lslq.jl b/src/lslq.jl
index 6e956e513..a3b4307b2 100644
--- a/src/lslq.jl
+++ b/src/lslq.jl
@@ -90,25 +90,25 @@ In this case, `N` can still be specified and indicates the weighted norm in whic
 
 #### Keyword arguments
 
-* `M`:
-* `N`:
-* `ldiv`:
-* `window`:
-* `transfer_to_lsqr`:
-* `sqd`:
-* `λ`:
-* `σ`:
-* `etol`:
-* `utol`:
-* `btol`:
-* `conlim`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `m` used for centered preconditioning of the augmented system;
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning of the augmented system;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `window`: number of iterations used to accumulate a lower bound on the error;
+* `transfer_to_lsqr`: transfer from the LSLQ point to the LSQR point, when it exists. The transfer is based on the residual norm;
+* `sqd`: if `true`, set `λ=1` for Hermitian quasi-definite systems;
+* `λ`: regularization parameter;
+* `σ`: strict lower bound on the smallest positive singular value `σₘᵢₙ` such as `σ = (1-10⁻⁷)σₘᵢₙ`;
+* `etol`: stopping tolerance based on the lower bound on the error;
+* `utol`: stopping tolerance based on the upper bound on the error;
+* `btol`: stopping tolerance used to detect zero-residual problems;
+* `conlim`: limit on the estimated condition number of `A` beyond which the solution will be abandoned;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/lsmr.jl b/src/lsmr.jl
index 0d3127566..b9efa6237 100644
--- a/src/lsmr.jl
+++ b/src/lsmr.jl
@@ -94,24 +94,24 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `N`:
-* `ldiv`:
-* `window`:
-* `sqd`:
-* `λ`:
-* `radius`:
-* `etol`:
-* `axtol`:
-* `btol`:
-* `conlim`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `m` used for centered preconditioning of the augmented system;
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning of the augmented system;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `window`: number of iterations used to accumulate a lower bound on the error;
+* `sqd`: if `true`, set `λ=1` for Hermitian quasi-definite systems;
+* `λ`: regularization parameter;
+* `radius`: add the trust-region constraint ‖x‖ ≤ `radius` if `radius > 0`. Useful to compute a step in a trust-region method for optimization;
+* `etol`: stopping tolerance based on the lower bound on the error;
+* `axtol`: tolerance on the backward error;
+* `btol`: stopping tolerance used to detect zero-residual problems;
+* `conlim`: limit on the estimated condition number of `A` beyond which the solution will be abandoned;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/lsqr.jl b/src/lsqr.jl
index 6ac4153d1..39a044deb 100644
--- a/src/lsqr.jl
+++ b/src/lsqr.jl
@@ -90,24 +90,24 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `N`:
-* `ldiv`:
-* `window`:
-* `sqd`:
-* `λ`:
-* `radius`:
-* `etol`:
-* `axtol`:
-* `btol`:
-* `conlim`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `m` used for centered preconditioning of the augmented system;
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning of the augmented system;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `window`: number of iterations used to accumulate a lower bound on the error;
+* `sqd`: if `true`, set `λ=1` for Hermitian quasi-definite systems;
+* `λ`: regularization parameter;
+* `radius`: add the trust-region constraint ‖x‖ ≤ `radius` if `radius > 0`. Useful to compute a step in a trust-region method for optimization;
+* `etol`: stopping tolerance based on the lower bound on the error;
+* `axtol`: tolerance on the backward error;
+* `btol`: stopping tolerance used to detect zero-residual problems;
+* `conlim`: limit on the estimated condition number of `A` beyond which the solution will be abandoned;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/minres.jl b/src/minres.jl
index cc94b4548..ba24ee184 100644
--- a/src/minres.jl
+++ b/src/minres.jl
@@ -71,19 +71,19 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `window`:
-* `λ`:
-* `atol`:
-* `rtol`:
-* `etol`:
-* `conlim`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `window`: number of iterations used to accumulate a lower bound on the error;
+* `λ`: regularization parameter;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `etol`: stopping tolerance based on the lower bound on the error;
+* `conlim`: limit on the estimated condition number of `A` beyond which the solution will be abandoned;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/minres_qlp.jl b/src/minres_qlp.jl
index c6a6173de..09c32c5bf 100644
--- a/src/minres_qlp.jl
+++ b/src/minres_qlp.jl
@@ -53,17 +53,17 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `Artol`:
-* `λ`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `Artol`: relative stopping tolerance based on the Aᴴ-residual norm;
+* `λ`: regularization parameter;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/qmr.jl b/src/qmr.jl
index eb6c82dbd..c23a829f5 100644
--- a/src/qmr.jl
+++ b/src/qmr.jl
@@ -53,14 +53,14 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `c`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `c`: the second initial vector of length `n` required by the Lanczos biorthogonalization process;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/symmlq.jl b/src/symmlq.jl
index 2b738f49c..175082268 100644
--- a/src/symmlq.jl
+++ b/src/symmlq.jl
@@ -54,21 +54,21 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `ldiv`:
-* `window`:
-* `transfer_to_cg`:
-* `λ`:
-* `λest`:
-* `etol`:
-* `conlim`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning;
+* `ldiv`: define whether the preconditioner uses `ldiv!` or `mul!`;
+* `window`: number of iterations used to accumulate a lower bound on the error;
+* `transfer_to_cg`: transfer from the SYMMLQ point to the CG point, when it exists. The transfer is based on the residual norm;
+* `λ`: regularization parameter;
+* `λest`: positive strict lower bound on the smallest eigenvalue `λₘᵢₙ` when solving a positive-definite system, such as `λest = (1-10⁻⁷)λₘᵢₙ`;
+* `etol`: stopping tolerance based on the lower bound on the error;
+* `conlim`: limit on the estimated condition number of `A` beyond which the solution will be abandoned;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `2n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/tricg.jl b/src/tricg.jl
index 84a869670..61f3389c8 100644
--- a/src/tricg.jl
+++ b/src/tricg.jl
@@ -75,20 +75,20 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `N`:
-* `ldiv`:
-* `spd`:
-* `snd`:
-* `flip`:
-* `τ` and `ν`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `m` used for centered preconditioning of the partitioned system;
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning of the partitioned system;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `spd`: if `true`, set `τ = 1` and `ν = 1` for Hermitian and positive-definite linear system;
+* `snd`: if `true`, set `τ = -1` and `ν = -1` for Hermitian and negative-definite linear systems;
+* `flip`: if `true`, set `τ = -1` and `ν = 1` for another known variant of Hermitian quasi-definite systems;
+* `τ` and `ν`: diagonal scaling factors of the partitioned Hermitian linear system;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/trilqr.jl b/src/trilqr.jl
index 2f051ae52..4fb2d6cce 100644
--- a/src/trilqr.jl
+++ b/src/trilqr.jl
@@ -53,14 +53,14 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `transfer_to_usymcg`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `transfer_to_usymcg`: transfer from the USYMLQ point to the USYMCG point, when it exists. The transfer is based on the residual norm;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/trimr.jl b/src/trimr.jl
index 2e0429513..4be1eb444 100644
--- a/src/trimr.jl
+++ b/src/trimr.jl
@@ -75,21 +75,21 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `M`:
-* `N`:
-* `ldiv`:
-* `spd`:
-* `snd`:
-* `flip`:
-* `sp`:
-* `τ` and `ν`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `M`: linear operator that models a Hermitian positive-definite matrix of size `m` used for centered preconditioning of the partitioned system;
+* `N`: linear operator that models a Hermitian positive-definite matrix of size `n` used for centered preconditioning of the partitioned system;
+* `ldiv`: define whether the preconditioners use `ldiv!` or `mul!`;
+* `spd`: if `true`, set `τ = 1` and `ν = 1` for Hermitian and positive-definite linear system;
+* `snd`: if `true`, set `τ = -1` and `ν = -1` for Hermitian and negative-definite linear systems;
+* `flip`: if `true`, set `τ = -1` and `ν = 1` for another known variant of Hermitian quasi-definite systems;
+* `sp`: if `true`, set `τ = 1` and `ν = 0` for saddle-point systems;
+* `τ` and `ν`: diagonal scaling factors of the partitioned Hermitian linear system;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/usymlq.jl b/src/usymlq.jl
index b7c823eaa..db092c5a2 100644
--- a/src/usymlq.jl
+++ b/src/usymlq.jl
@@ -61,14 +61,14 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `transfer_to_usymcg`:
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `transfer_to_usymcg`: transfer from the USYMLQ point to the USYMCG point, when it exists. The transfer is based on the residual norm;
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments
 
diff --git a/src/usymqr.jl b/src/usymqr.jl
index f1783cdee..471fa5313 100644
--- a/src/usymqr.jl
+++ b/src/usymqr.jl
@@ -58,13 +58,13 @@ and `false` otherwise.
 
 #### Keyword arguments
 
-* `atol`:
-* `rtol`:
-* `itmax`:
-* `verbose`:
-* `history`:
-* `callback`:
-* `iostream`:
+* `atol`: absolute stopping tolerance based on the residual norm;
+* `rtol`: relative stopping tolerance based on the residual norm;
+* `itmax`: the maximum number of iterations. If `itmax=0`, the default number of iterations is set to `m+n`;
+* `verbose`: additional details can be displayed if verbose mode is enabled (verbose > 0). Information will be displayed every `verbose` iterations;
+* `history`: collect additional statistics on the run such as residual norms, or Aᴴ-residual norms;
+* `callback`: function or functor called as `callback(solver)` that returns `true` if the Krylov method should terminate, and `false` otherwise;
+* `iostream`: stream to which output is logged.
 
 #### Output arguments