A note on modified iterative methods for consistent linear systems

Abstract

A considerable improvement in convergence rate can be obtained by performing certain row operations on the linear system Ax = b before applying the Gauss-Seidel (GS) or Jacobi iterative methods when A is a non-singular M matrix or singular tridiagonal Q matrix [2]. In this paper we prove that this modified method also improves the convergence for another class of matrices and that the modified GS and Jacobi methods always converge even when the standard GS and Jacobi methods fail to converge.

Keywords:

• Jacobi
• Gauss-Seidel
• iterative methods
• Z matrix

C.R. Categories:

• G.1.3.