From c0fa5ca32d48f67643f500137b6967bc2983ec5c Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Tue, 15 Oct 2019 13:43:34 -0400
Subject: [PATCH] Remark about USYMCG

---
 src/bilq.jl   | 2 +-
 src/usymlq.jl | 4 ++++
 src/usymqr.jl | 1 +
 3 files changed, 6 insertions(+), 1 deletion(-)

diff --git a/src/bilq.jl b/src/bilq.jl
index 915f6f5b5..a7692ce76 100644
--- a/src/bilq.jl
+++ b/src/bilq.jl
@@ -61,7 +61,7 @@ function bilq(A :: AbstractLinearOperator, b :: AbstractVector{T}; c :: Abstract
   ζₖ₋₁ = ζbarₖ = zero(T)     # ζₖ₋₁ and ζbarₖ are the last components of z̅ₖ = (L̅ₖ)⁻¹β₁e₁
   ζₖ₋₂ = ηₖ = zero(T)        # ζₖ₋₂ and ηₖ are used to update ζₖ₋₁ and ζbarₖ
   δbarₖ₋₁ = δbarₖ = zero(T)  # Coefficients of Lₖ₋₁ and L̅ₖ modified during two iterations
-  norm_vₖ = bNorm / βₖ       # ‖vₖ‖ used for residual norm estimates
+  norm_vₖ = bNorm / βₖ       # ‖vₖ‖ is used for residual norm estimates
 
   # Stopping criterion.
   solved_lq = bNorm ≤ ε
diff --git a/src/usymlq.jl b/src/usymlq.jl
index 96616a59d..7847cadaa 100644
--- a/src/usymlq.jl
+++ b/src/usymlq.jl
@@ -22,11 +22,15 @@ export usymlq
 """Solve the linear system Ax = b using the USYMLQ method.
 
 USYMLQ is based on a tridiagonalization process for unsymmetric matrices.
+The eror norm ‖x - x*‖ monotonously decreases in USYMLQ.
 It's considered as a generalization of SYMMLQ.
 
 It can also be applied to under-determined and over-determined problems.
 In all cases, problems must be consistent.
 
+An option gives the possibility of transferring to the USYMCG point,
+when it exists. The transfer is based on the residual norm.
+
 This version of USYMLQ works in any floating-point data type.
 """
 function usymlq(A :: AbstractLinearOperator, b :: AbstractVector{T}, c :: AbstractVector{T};
diff --git a/src/usymqr.jl b/src/usymqr.jl
index abcfefc31..ff1802121 100644
--- a/src/usymqr.jl
+++ b/src/usymqr.jl
@@ -22,6 +22,7 @@ export usymqr
 """Solve the linear system Ax = b using the USYMQR method.
 
 USYMQR is based on a tridiagonalization process for unsymmetric matrices.
+The residual norm ‖b - Ax‖ monotonously decreases in USYMQR.
 It's considered as a generalization of MINRES.
 
 It can also be applied to under-determined and over-determined problems.