Computational experience with globally convergent descent methods for large sparse systems of nonlinear equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 1998-01-01 DOI:10.1080/10556789808805677

L. Luksan, J. Vlček

引用次数: 23

Abstract

This paper is devoted to globally convergent Armijo-type descent methods for solving large sparse systems of nonlinear equations. These methods include the discrete Newtcin method and a broad class of Newton-like methods based on various approximations of the Jacobian matrix. We propose a general theory of global convergence together with a robust algorithm including a special restarting strategy. This algorithm is based cfn the preconditioned smoothed CGS method for solving nonsymmetric systems of linejtr equations. After reviewing 12 particular Newton-like methods, we propose results of extensive computational experiments. These results demonstrate high efficiency of tip proposed algorithm

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大型非线性方程稀疏系统全局收敛下降法的计算经验

研究了求解大型非线性方程稀疏系统的全局收敛armijo型下降方法。这些方法包括离散牛顿法和基于雅可比矩阵的各种近似的一类类牛顿方法。我们提出了一个全局收敛的一般理论和一个包含特殊重启策略的鲁棒算法。该算法基于求解非对称线性方程组的预条件光滑CGS法。在回顾了12种特定的类牛顿方法后，我们提出了广泛的计算实验结果。实验结果表明，该算法具有较高的效率

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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