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Volume 21, Issue 2
Modified Newton-NDSS Method for Solving Nonlinear System with Complex Symmetric Jacobian Matrices

Xiaohui Yu & Qingbiao Wu

DOI: 10.4208/ijnam2024-1012

Int. J. Numer. Anal. Mod., 21 (2024), pp. 295-314.

Published online: 2024-04

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  • Abstract

An efficient iteration method is provided in this paper for solving a class of nonlinear systems whose Jacobian matrices are complex and symmetric. The modified Newton-NDSS method is developed and applied to the class of nonlinear systems by adopting the modified Newton method as the outer solver and a new double-step splitting (NDSS) iteration scheme as the inner solver. Additionally, we theoretically analyze the local convergent properties of the new method under the weaker Hölder conditions. Lastly, the new method is compared numerically with some existing ones and the numerical experiments solving the nonlinear equations demonstrate the superiority of the Newton-NDSS method.

  • Keywords

Modified Newton-NDSS method, complex nonlinear systems, Hölder continuous condition, symmetric Jacobian matrix, convergence analysis.

  • AMS Subject Headings

65B99, 65N12, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-21-295, author = {Yu , Xiaohui and Wu , Qingbiao}, title = {Modified Newton-NDSS Method for Solving Nonlinear System with Complex Symmetric Jacobian Matrices}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2024}, volume = {21}, number = {2}, pages = {295--314}, abstract = {

An efficient iteration method is provided in this paper for solving a class of nonlinear systems whose Jacobian matrices are complex and symmetric. The modified Newton-NDSS method is developed and applied to the class of nonlinear systems by adopting the modified Newton method as the outer solver and a new double-step splitting (NDSS) iteration scheme as the inner solver. Additionally, we theoretically analyze the local convergent properties of the new method under the weaker Hölder conditions. Lastly, the new method is compared numerically with some existing ones and the numerical experiments solving the nonlinear equations demonstrate the superiority of the Newton-NDSS method.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1012}, url = {http://global-sci.org/intro/article_detail/ijnam/23028.html} }
TY - JOUR T1 - Modified Newton-NDSS Method for Solving Nonlinear System with Complex Symmetric Jacobian Matrices AU - Yu , Xiaohui AU - Wu , Qingbiao JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 295 EP - 314 PY - 2024 DA - 2024/04 SN - 21 DO - http://doi.org/10.4208/ijnam2024-1012 UR - https://global-sci.org/intro/article_detail/ijnam/23028.html KW - Modified Newton-NDSS method, complex nonlinear systems, Hölder continuous condition, symmetric Jacobian matrix, convergence analysis. AB -

An efficient iteration method is provided in this paper for solving a class of nonlinear systems whose Jacobian matrices are complex and symmetric. The modified Newton-NDSS method is developed and applied to the class of nonlinear systems by adopting the modified Newton method as the outer solver and a new double-step splitting (NDSS) iteration scheme as the inner solver. Additionally, we theoretically analyze the local convergent properties of the new method under the weaker Hölder conditions. Lastly, the new method is compared numerically with some existing ones and the numerical experiments solving the nonlinear equations demonstrate the superiority of the Newton-NDSS method.

Yu , Xiaohui and Wu , Qingbiao. (2024). Modified Newton-NDSS Method for Solving Nonlinear System with Complex Symmetric Jacobian Matrices. International Journal of Numerical Analysis and Modeling. 21 (2). 295-314. doi:10.4208/ijnam2024-1012
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