A new iterative method for large sparse linear systems

Abstract

In this paper a new iterative method is given for solving large sparse linear system. The new iterative method involves a parameter p and an auxiliary matrix P. The method is shown to be convergent if p and matrix P are properly chosen and if the coefficient matrix of the concerned linear system is nonsingular. The new method is also suitable for parallel computations and can be applied to least squares problems, optimization problems and others. Besides, the new iterative method can be combined with preconditioning techniques, therefore can be expected to be more attractive.

Keywords:

• Linear systems
• iterative method
• Gauss-Seidel method
• SOR method
• conjugate gradient method
• parallel computations and preconditioning techniques

C.R. Categories:

• G.1.3