Apostolos Hadjidimos,
Xiezhang Li,
Richard S. Varga
S. A1 - A14
doi:
10.1553/etna_vol60sA1
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol60sA1
Abstract:
Assume that $A\in{C}^{n\times n}$ is a block $p$-cyclic consistently ordered matrixand that its associated Jacobiiteration matrix $B$, which is weakly cyclic of index $p$, haseigenvalues $\mu$ whose $p$th powers are all realnonpositive (resp. nonnegative). Usually, one is interestedonly in the relaxation parameter $\omega$ that minimizes the spectral radiusof the iteration matrix of the associated SOR iterative method, but here weare interested in all real values for the relaxation parameter$\omega$ for which the SOR iteration matrix is convergent. This will beachieved for the values of $p=2,3,4,\ldots,$ and for $p\rightarrow\infty.$
block p-cyclic matrix, weakly cyclic of index p matrix, block Jacobi and SOR iteration matrices, Schur–Cohn Algorithm
Published Online:
2024/01/15 15:01:42
Object Identifier:
0xc1aa5576 0x003ec1b1
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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