Volume 16, Issue 4
The Multi-Parameters Overrelaxation Method
DOI:

J. Comp. Math., 16 (1998), pp. 367-374

Published online: 1998-08

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• Abstract

In this paper, first, we present the comparison theorem and the (generalized) Stein-Rosenberg theorem for the GMPOR method, which improves some recent results$^{[9,11,13]}$. Second, we also give the convergent theorem of the GMPOR method, which generalizes the corresponding result of [9]. Finally, we provide the real interval such that the generalized extrapolated Jacobi iterative method and the generalized SOR methods simultaneously converge, one of the main results in [1] is extended.

• Keywords

GMPOR iterative method convergence comparison theorem Stein-Rosenberg theorem

• AMS Subject Headings

@Article{JCM-16-367, author = {}, title = {The Multi-Parameters Overrelaxation Method}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {4}, pages = {367--374}, abstract = { In this paper, first, we present the comparison theorem and the (generalized) Stein-Rosenberg theorem for the GMPOR method, which improves some recent results$^{[9,11,13]}$. Second, we also give the convergent theorem of the GMPOR method, which generalizes the corresponding result of [9]. Finally, we provide the real interval such that the generalized extrapolated Jacobi iterative method and the generalized SOR methods simultaneously converge, one of the main results in [1] is extended. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9167.html} }
TY - JOUR T1 - The Multi-Parameters Overrelaxation Method JO - Journal of Computational Mathematics VL - 4 SP - 367 EP - 374 PY - 1998 DA - 1998/08 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9167.html KW - GMPOR iterative method KW - convergence KW - comparison theorem KW - Stein-Rosenberg theorem AB - In this paper, first, we present the comparison theorem and the (generalized) Stein-Rosenberg theorem for the GMPOR method, which improves some recent results$^{[9,11,13]}$. Second, we also give the convergent theorem of the GMPOR method, which generalizes the corresponding result of [9]. Finally, we provide the real interval such that the generalized extrapolated Jacobi iterative method and the generalized SOR methods simultaneously converge, one of the main results in [1] is extended.