Version 1.3.1

2nd December 2015

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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 × n unsymmetric linear system Ax = b, optionally using preconditioning. If PL, PR are left and right preconditioning matrices, the routine actually solves the preconditioned system

Āx̄ = b̄,

with Ā = PLAPR and b̄ = PLb. The solution may be recovered as x = PRx̄. If PL = I, preconditioning is said to be from the right, if PR = 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.