The extrapolated gauss-seidel plus semi-iterative method for generalized consistently ordered matrices

Abstract

This paper discusses the Extrapolated Gauss-Seidel method with semi-iterative techniques to solve large sparse linear systems of the form Ax = b, when A is a generalized consistently ordered (GCO (p– 1,1)) matrix, (see [3], [2]) and the pth power of the Jacobi iterative matrix B possesses non-negative eigenvalues. The theoretical results demonstrate that the combination of the extrapolated Gauss-Seidel method with the semi-iterative strategy is competitive with the SOR method, and the larger p is, the better the method becomes.

Keywords:

• Extrapolated gauss-seidel method
• semi-iterative method
• general­ ized consistently ordered matrix (gco)
• spectral radius
• asymptotic convergence rate
• virtual spectral radius
• quasi-average convergence rate
• virtual asymptotic quasi-average convergence rate

C.R. Categories:

• G1.3

^*Shenyang Institute of Computing Technology, Academia Sinica, Shenyang, China.

^*Shenyang Institute of Computing Technology, Academia Sinica, Shenyang, China.

Notes

^*Shenyang Institute of Computing Technology, Academia Sinica, Shenyang, China.