An Iterative Method for Nonsymmetric Systems with Multiple Right-Hand Sides
Valeria Simoncini, Efstratios Gallopoulos · SIAM Journal on Scientific Computing · 1995
We propose a method for the solution of linear systems $AX = B$ where A is a large, possibly sparse, nonsymmetric matrix of order n, and B is an arbitrary rectangular matrix of order $n \times s$ with s of moderate size. The method uses a single Krylov subspace per step as a generator of approximations, a projection process, and a Richardson acceleration technique. It thus combines the advantages of recent hybrid methods with those for solving symmetric systems with multiple right-hand sides. Numerical experiments indicate that in several cases the method has better practical performance and significantly lower memory requirements than block versions of nonsymmetric solvers and other proposed methods for the solution of systems with multiple right-hand sides.