## Version 1.3.1

2nd December 2015

Recent Changes

This routine uses the Generalized Minimal Residual method with restarts every $m$ iterations, GMRES($m$), to solve the $n×n$ unsymmetric linear system $Ax=b$, optionally using preconditioning. If ${P}_{L}$, ${P}_{R}$ are left and right preconditioning matrices, the routine actually solves the preconditioned system
$\stackrel{̄}{A}\stackrel{̄}{x}=\stackrel{̄}{b},$
with $\stackrel{̄}{A}={P}_{L}A{P}_{R}$ and $\stackrel{̄}{b}={P}_{L}b$. The solution may be recovered as $x={P}_{R}\stackrel{̄}{x}$. If ${P}_{L}=I$, preconditioning is said to be from the right, if ${P}_{R}=I$, it is said to be from the left, and otherwise it is from both sides. Reverse communication is used for preconditioning operations and matrix-vector products of the form $Az$.