MI24 — Unsymmetric system: GMRES (generalized minimal residual) method

Version 1.3.1

2nd December 2015

User documentation

Fortran

Single
Double

MI24 Unsymmetric system: GMRES (generalized minimal residual) method

This routine uses the Generalized Minimal Residual method with restarts every $m$ iterations, GMRES( $m$ ), to solve the $n \times n$ unsymmetric linear system $A x = b$ , optionally using preconditioning. If $P_{L}$ , $P_{R}$ are left and right preconditioning matrices, the routine actually solves the preconditioned system

\bar{A} \bar{x} = \bar{b},

with $\bar{A} = P_{L} A P_{R}$ and $\bar{b} = P_{L} b$ . The solution may be recovered as $x = P_{R} \bar{x}$ . 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 $A z$ .