On the Convergence of the Modified Accelerated Overrelaxation (Maor) Method
| dc.contributor.author | Hadjidimos, A. | en |
| dc.contributor.author | Psimarni, A. | en |
| dc.contributor.author | Yeyios, A. K. | en |
| dc.date.accessioned | 2015-11-24T17:26:33Z | |
| dc.date.available | 2015-11-24T17:26:33Z | |
| dc.identifier.issn | 0168-9274 | - |
| dc.identifier.uri | https://olympias.lib.uoi.gr/jspui/handle/123456789/13225 | |
| dc.rights | Default Licence | - |
| dc.subject | p-cyclic matrices | en |
| dc.subject | iterative methods | en |
| dc.subject | linear-systems | en |
| dc.title | On the Convergence of the Modified Accelerated Overrelaxation (Maor) Method | en |
| heal.abstract | In this paper we introduce the Modified Accelerated Overrelaxation (MAOR) method, a generalization of the AOR one, for the iterative solution of the nonsingular linear system Ax = b. We assume that A is in a p x p partitioned form and belongs to a subclass of the p-cyclic consistently ordered matrices. It is pointed out that for specific choices of the "acceleration" and "relaxation" matrices the MAOR method reduces to an extrapolation of the Jacobi or of the Modified (M)SOR method with different parameters corresponding to the row blocks of A. First, an eigenvalue relationship connecting the spectra of the block Jacobi and MAOR matrices associated with A is derived from which many well-known eigenvalue relationships can be recovered. Then, by considering the particular case p = 2 it is shown that a matrix analogue of the aforementioned eigenvalue relationship holds and the MAOR method is equivalent to a certain two-step one. Finally, the precise domains of convergence of the MAOR method are derived, when the spectrum of the Jacobi matrix is real or pure imaginary and a brief discussion follows which concludes the present study. | en |
| heal.access | campus | - |
| heal.fullTextAvailability | TRUE | - |
| heal.identifier.secondary | <Go to ISI>://A1992JD49100002 | - |
| heal.identifier.secondary | http://ac.els-cdn.com/016892749290034B/1-s2.0-016892749290034B-main.pdf?_tid=2d717135baea5bcf8e14b0aa59a0b13e&acdnat=1339396664_4ef2fbaccf91fde7370c6d814877b407 | - |
| heal.journalName | Applied Numerical Mathematics | en |
| heal.journalType | peer reviewed | - |
| heal.language | en | - |
| heal.publicationDate | 1992 | - |
| heal.publisher | Elsevier | en |
| heal.recordProvider | Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών | el |
| heal.type | journalArticle | - |
| heal.type.el | Άρθρο Περιοδικού | el |
| heal.type.en | Journal article | en |
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