Block AOR iteration for nonsymmetric matrices

Author:
Theodore S. Papatheodorou

Journal:
Math. Comp. **41** (1983), 511-525

MSC:
Primary 65F50; Secondary 65F10

DOI:
https://doi.org/10.1090/S0025-5718-1983-0717699-0

MathSciNet review:
717699

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Abstract: We consider a class of matrices that are of interest to numerical applications and are large, sparse, but not symmetric or diagonally dominant. We give a criterion for the existence of (and we actually construct) the inverse matrix in terms of powers of a "small" matrix. We use this criterion to find that the spectral radius of the Jacobi iteration matrix, corresponding to a block tridiagonal partition, is in general . We also derive conditions (that are satisfied in cases of interest to applications) for the Jacobi matrix to have spectral radius = 1. We introduce convergent "block **AOR**" iterative schemes such as extrapolated Jacobi and extrapolated Gauss-Seidel schemes with optimum (under) relaxation parameter . A numerical example pertaining to the solution of Poisson's equation is given, as a demonstration of some of our hypotheses and results. A comparison with **SOR**, applied to the 5-point finite difference method, is also included.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1983-0717699-0

Keywords:
**AOR** iteration

Article copyright:
© Copyright 1983
American Mathematical Society