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Volume 6, Issue 4
A Class of Preconditioned TGHSS-Based Iteration Methods for Weakly Nonlinear Systems

Min-Li Zeng & Guo-Feng Zhang

DOI: 10.4208/eajam.150116.240516a

East Asian J. Appl. Math., 6 (2016), pp. 367-383.

Published online: 2018-02

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  • Abstract

In this paper, we first construct a preconditioned two-parameter generalized Hermitian and skew-Hermitian splitting (PTGHSS) iteration method based on the two-parameter generalized Hermitian and skew-Hermitian splitting (TGHSS) iteration method for non-Hermitian positive definite linear systems. Then a class of PTGHSS-based iteration methods are proposed for solving weakly nonlinear systems based on separable property of the linear and nonlinear terms. The conditions for guaranteeing the local convergence are studied and the quasi-optimal iterative parameters are derived. Numerical experiments are implemented to show that the new methods are feasible and effective for large scale systems of weakly nonlinear systems.

  • Keywords

System of weakly nonlinear equations, GHSS iteration method, local convergence, inner iteration, outer iteration.

  • AMS Subject Headings

65F10, 65F50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-6-367, author = {Min-Li Zeng and Guo-Feng Zhang}, title = {A Class of Preconditioned TGHSS-Based Iteration Methods for Weakly Nonlinear Systems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {6}, number = {4}, pages = {367--383}, abstract = {

In this paper, we first construct a preconditioned two-parameter generalized Hermitian and skew-Hermitian splitting (PTGHSS) iteration method based on the two-parameter generalized Hermitian and skew-Hermitian splitting (TGHSS) iteration method for non-Hermitian positive definite linear systems. Then a class of PTGHSS-based iteration methods are proposed for solving weakly nonlinear systems based on separable property of the linear and nonlinear terms. The conditions for guaranteeing the local convergence are studied and the quasi-optimal iterative parameters are derived. Numerical experiments are implemented to show that the new methods are feasible and effective for large scale systems of weakly nonlinear systems.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.150116.240516a}, url = {http://global-sci.org/intro/article_detail/eajam/10805.html} }
TY - JOUR T1 - A Class of Preconditioned TGHSS-Based Iteration Methods for Weakly Nonlinear Systems AU - Min-Li Zeng & Guo-Feng Zhang JO - East Asian Journal on Applied Mathematics VL - 4 SP - 367 EP - 383 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.150116.240516a UR - https://global-sci.org/intro/article_detail/eajam/10805.html KW - System of weakly nonlinear equations, GHSS iteration method, local convergence, inner iteration, outer iteration. AB -

In this paper, we first construct a preconditioned two-parameter generalized Hermitian and skew-Hermitian splitting (PTGHSS) iteration method based on the two-parameter generalized Hermitian and skew-Hermitian splitting (TGHSS) iteration method for non-Hermitian positive definite linear systems. Then a class of PTGHSS-based iteration methods are proposed for solving weakly nonlinear systems based on separable property of the linear and nonlinear terms. The conditions for guaranteeing the local convergence are studied and the quasi-optimal iterative parameters are derived. Numerical experiments are implemented to show that the new methods are feasible and effective for large scale systems of weakly nonlinear systems.

Min-Li Zeng and Guo-Feng Zhang. (2018). A Class of Preconditioned TGHSS-Based Iteration Methods for Weakly Nonlinear Systems. East Asian Journal on Applied Mathematics. 6 (4). 367-383. doi:10.4208/eajam.150116.240516a
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