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Volume 11, Issue 2
An Efficient Iterative Approach to Large Sparse Nonlinear Systems with Non-Hermitian Jacobian Matrices

Min-Hong Chen, Qing-Biao Wu, Qin Gao & Rong-Fei Lin

DOI: 10.4208/eajam.260420.171120

East Asian J. Appl. Math., 11 (2021), pp. 349-368.

Published online: 2021-02

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  • Abstract

Inner-outer iterative methods for large sparse non-Hermitian nonlinear systems are considered. Using the ideas of modified generalised Hermitian and skew Hermitian methods and double-parameter GHSS method, we develop a double-parameter modified generalised Hermitian and skew Hermitian method (DMGHSS) for linear non-Hermitian systems. Using this method as the inner iterations and the modified Newton method as the outer iterations, we introduce modified Newton-DMGHSS methods for large sparse non-Hermitian nonlinear systems. The convergence of the methods is studied. Numerical results demonstrate the efficacy of the methods.

  • Keywords

Splitting iteration, positive definite Jacobian matrices, large sparse nonlinear system, modified Newton-DMGHSS method, convergence.

  • AMS Subject Headings

65F10, 65F50, 65H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-349, author = {Chen , Min-HongWu , Qing-BiaoGao , Qin and Lin , Rong-Fei}, title = {An Efficient Iterative Approach to Large Sparse Nonlinear Systems with Non-Hermitian Jacobian Matrices}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {11}, number = {2}, pages = {349--368}, abstract = {

Inner-outer iterative methods for large sparse non-Hermitian nonlinear systems are considered. Using the ideas of modified generalised Hermitian and skew Hermitian methods and double-parameter GHSS method, we develop a double-parameter modified generalised Hermitian and skew Hermitian method (DMGHSS) for linear non-Hermitian systems. Using this method as the inner iterations and the modified Newton method as the outer iterations, we introduce modified Newton-DMGHSS methods for large sparse non-Hermitian nonlinear systems. The convergence of the methods is studied. Numerical results demonstrate the efficacy of the methods.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.260420.171120}, url = {http://global-sci.org/intro/article_detail/eajam/18638.html} }
TY - JOUR T1 - An Efficient Iterative Approach to Large Sparse Nonlinear Systems with Non-Hermitian Jacobian Matrices AU - Chen , Min-Hong AU - Wu , Qing-Biao AU - Gao , Qin AU - Lin , Rong-Fei JO - East Asian Journal on Applied Mathematics VL - 2 SP - 349 EP - 368 PY - 2021 DA - 2021/02 SN - 11 DO - http://doi.org/10.4208/eajam.260420.171120 UR - https://global-sci.org/intro/article_detail/eajam/18638.html KW - Splitting iteration, positive definite Jacobian matrices, large sparse nonlinear system, modified Newton-DMGHSS method, convergence. AB -

Inner-outer iterative methods for large sparse non-Hermitian nonlinear systems are considered. Using the ideas of modified generalised Hermitian and skew Hermitian methods and double-parameter GHSS method, we develop a double-parameter modified generalised Hermitian and skew Hermitian method (DMGHSS) for linear non-Hermitian systems. Using this method as the inner iterations and the modified Newton method as the outer iterations, we introduce modified Newton-DMGHSS methods for large sparse non-Hermitian nonlinear systems. The convergence of the methods is studied. Numerical results demonstrate the efficacy of the methods.

Chen , Min-HongWu , Qing-BiaoGao , Qin and Lin , Rong-Fei. (2021). An Efficient Iterative Approach to Large Sparse Nonlinear Systems with Non-Hermitian Jacobian Matrices. East Asian Journal on Applied Mathematics. 11 (2). 349-368. doi:10.4208/eajam.260420.171120
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