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Volume 13, Issue 1
A Class of Relaxed TTSCSP Iteration Methods for Weakly Nonlinear Systems

Xiaohui Yu & Qingbiao Wu

DOI: 10.4208/eajam.291121.090722

East Asian J. Appl. Math., 13 (2023), pp. 76-94.

Published online: 2023-01

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  • Abstract

A relaxed TTSCSP (RTTSCSP) iteration method for complex linear systems is constructed. Based on the strong dominance and separability of linear and nonlinear terms, Picard-RTTSCSP and nonlinear RTTSCSP-like iterative methods are developed and applied to complex systems of weakly nonlinear equations. The convergence of the method is investigated. Besides, optimal iterative parameters minimizing the upper bound of the spectral radius are derived. Numerical examples show the effectiveness and applicability of the methods to complex systems of weakly nonlinear equations.

  • Keywords

Picard-RTTSCSP method, nonlinear RTTSCSP-like method, weakly nonlinear system, convergence.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-13-76, author = {Yu , Xiaohui and Wu , Qingbiao}, title = {A Class of Relaxed TTSCSP Iteration Methods for Weakly Nonlinear Systems}, journal = {East Asian Journal on Applied Mathematics}, year = {2023}, volume = {13}, number = {1}, pages = {76--94}, abstract = {

A relaxed TTSCSP (RTTSCSP) iteration method for complex linear systems is constructed. Based on the strong dominance and separability of linear and nonlinear terms, Picard-RTTSCSP and nonlinear RTTSCSP-like iterative methods are developed and applied to complex systems of weakly nonlinear equations. The convergence of the method is investigated. Besides, optimal iterative parameters minimizing the upper bound of the spectral radius are derived. Numerical examples show the effectiveness and applicability of the methods to complex systems of weakly nonlinear equations.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.291121.090722 }, url = {http://global-sci.org/intro/article_detail/eajam/21303.html} }
TY - JOUR T1 - A Class of Relaxed TTSCSP Iteration Methods for Weakly Nonlinear Systems AU - Yu , Xiaohui AU - Wu , Qingbiao JO - East Asian Journal on Applied Mathematics VL - 1 SP - 76 EP - 94 PY - 2023 DA - 2023/01 SN - 13 DO - http://doi.org/10.4208/eajam.291121.090722 UR - https://global-sci.org/intro/article_detail/eajam/21303.html KW - Picard-RTTSCSP method, nonlinear RTTSCSP-like method, weakly nonlinear system, convergence. AB -

A relaxed TTSCSP (RTTSCSP) iteration method for complex linear systems is constructed. Based on the strong dominance and separability of linear and nonlinear terms, Picard-RTTSCSP and nonlinear RTTSCSP-like iterative methods are developed and applied to complex systems of weakly nonlinear equations. The convergence of the method is investigated. Besides, optimal iterative parameters minimizing the upper bound of the spectral radius are derived. Numerical examples show the effectiveness and applicability of the methods to complex systems of weakly nonlinear equations.

Yu , Xiaohui and Wu , Qingbiao. (2023). A Class of Relaxed TTSCSP Iteration Methods for Weakly Nonlinear Systems. East Asian Journal on Applied Mathematics. 13 (1). 76-94. doi:10.4208/eajam.291121.090722
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