求解具有复杂对称雅各布矩阵的非线性系统的修正牛顿-NDSS 方法

IF 1.3 4区数学 Q1 MATHEMATICS International Journal of Numerical Analysis and Modeling Pub Date : 2024-04-01 DOI:10.4208/ijnam2024-1012

Xiaohui Yu, Qingbiao Wu

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引用次数: 0

摘要

本文提供了一种高效的迭代法，用于求解一类雅各布矩阵复杂且对称的非线性系统。通过采用修正牛顿法作为外求解器和新的双步分裂（NDSS）迭代方案作为内求解器，开发了修正牛顿-NDSS 方法，并将其应用于该类非线性系统。此外，我们还从理论上分析了新方法在较弱的赫尔德条件下的局部收敛特性。最后，我们将新方法与一些现有方法进行了数值比较，并通过求解非线性方程的数值实验证明了牛顿-NDSS 方法的优越性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Modified Newton-NDSS Method for Solving Nonlinear System with Complex Symmetric Jacobian Matrices

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.

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来源期刊

International Journal of Numerical Analysis and Modeling 数学-数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is directed to the broad spectrum of researchers in numerical methods throughout science and engineering, and publishes high quality original papers in all fields of numerical analysis and mathematical modeling including: numerical differential equations, scientific computing, linear algebra, control, optimization, and related areas of engineering and scientific applications. The journal welcomes the contribution of original developments of numerical methods, mathematical analysis leading to better understanding of the existing algorithms, and applications of numerical techniques to real engineering and scientific problems. Rigorous studies of the convergence of algorithms, their accuracy and stability, and their computational complexity are appropriate for this journal. Papers addressing new numerical algorithms and techniques, demonstrating the potential of some novel ideas, describing experiments involving new models and simulations for practical problems are also suitable topics for the journal. The journal welcomes survey articles which summarize state of art knowledge and present open problems of particular numerical techniques and mathematical models.