Title

A Note on the SOR and USSOR Iterative Methods Applied to P-Cylic Matrices

Document Type

Contribution to Book

Publication Date

1990

Publication Title

Iterative Methods for Large Linear Systems

DOI

10.1016/B978-0-12-407475-0.50020-6

ISBN

978-0-12-407475-0

Abstract

In this note, we determine a new functional equation

[λ−(1−ω)(1−ω^)]p=λk[λω+ω^−ωω^]|ζL|−k[λω^+ω−ωω^]|ζU|−k⋅(ω+ω^−ωω^)2kμp,

which couples the nonzero eigenvalues of the USSOR (unsymmetric successive overrelaxation) iteration matrix Tω,ω with the eigenvalues of an associated block Jacobi matrix B in the p-cyclic case. Such function equations are of course direct descendants of the now famous functional equation

(λ+ω-1)2=λω2μ2

derived in 1950 by David M. Young, Jr. in his Harvard University thesis.

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