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.
Recommended Citation
Li, Xiezhang, Richard Varga.
1990.
"A Note on the SOR and USSOR Iterative Methods Applied to P-Cylic Matrices."
Iterative Methods for Large Linear Systems, David R. Kincaid and Linda J. Hayes (Ed.): 235-249: Elsevier Ltd..
doi: 10.1016/B978-0-12-407475-0.50020-6 isbn: 978-0-12-407475-0
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/568
