A new nonlinear ABS-type algorithm and its efficiency analysis ∗

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 1998-01-01 DOI:10.1080/10556789808805702

N. Deng, Z. Chen

引用次数: 2

Abstract

As a continuation work following [4] and [5], a new ABS-type algorithm for a nonlinear system of equations is proposed. A major iteration of this algorithm requires n component evaluations and only one gradient evaluation. We prove that the algorithm is superlinearly convergent with R-order at least τ n , where τ n is the unique positive root of τn −τn−1 −1=0. It is shown that the new algorithm is usually more efficient than the methods of Newton, Brown and Brent, and the ABS-type algorithms in [1], [4] and [5], in the sense of some standard efficiency measure.

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一种新的非线性abs型算法及其效率分析

作为继[4]和[5]之后的延续工作，提出了一种新的求解非线性方程组的abs型算法。该算法的一次主要迭代需要n个分量评估和一次梯度评估。我们证明了该算法在r阶至少τn下是超线性收敛的，其中τn是τn−τn−1−1=0的唯一正根。结果表明，在某种标准效率度量的意义上，新算法通常比Newton、Brown和Brent方法以及[1]、[4]和[5]中的abs型算法效率更高。

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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