基于概率雅各布模型的 Levenberg-Marquardt 算法的复杂性约束

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-07-18 DOI:10.1007/s11590-024-02140-x

Ruixue Zhao

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引用次数: 0

摘要

在本文中，我们提出了一种针对非线性方程的 Levenberg-Marquardt 算法，在这种非线性方程中，精确的 Jacobians 不可用，但其模型近似值可以通过某种随机方式建立。我们研究了该算法的复杂性，并证明获得一阶静止点的期望迭代次数上限为 \(O(\epsilon^{-3})\)。

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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Complexity bound of a Levenberg–Marquardt algorithm based on probabilistic Jacobian models

In this paper, we present a Levenberg–Marquardt algorithm for nonlinear equations, where the exact Jacobians are unavailable, but their model approximations can be built in some random fashion. We study the complexity of the algorithm and show that the upper bound of the iteration numbers in expectation to obtain a first order stationary point is \(O(\epsilon ^{-3})\).

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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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