Iterative Methods by SPD and Small Subspace Solvers for
Nonsymmetric or Indefinite Problems

Jinchao Xu
Deparpartment of Mathematics
Penn State University
University Park, PA 16802

Abstract

This paper is devoted to a class of iterative methods for solving nonsymmetric or indefinite problems that are dominated by some SPD (symmetric positive definite) problem. The algorithm is based on a direct solver for the original equation restricted on a small subspace and a given iterative method for the SPD equation. It is shown that any convergent iterative method for the SPD problem will give rise to an algorithm that converges with a comparable rate if the small subspace is properly chosen. Furthermore a number of preconditioners that can be used with GMRES type methods are also obtained.


Contributed January 7, 1993.