通过正交球形平滑法论无衍生莱文伯格-马夸特算法的全局复杂性

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Scientific Computing Pub Date : 2024-08-06 DOI:10.1007/s10915-024-02649-4

Xi Chen, Jinyan Fan

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引用次数: 0

摘要

本文针对非线性最小二乘法问题提出了一种无导数的 Levenberg-Marquardt 算法，通过正交球面平滑对雅各矩阵进行近似。结果表明，使用近似雅各矩阵的梯度模型在概率上是一阶精确的。同时还给出了算法的高概率复杂度约束。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On the Global Complexity of a Derivative-Free Levenberg-Marquardt Algorithm via Orthogonal Spherical Smoothing

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On the Global Complexity of a Derivative-Free Levenberg-Marquardt Algorithm via Orthogonal Spherical Smoothing

In this paper, we propose a derivative-free Levenberg-Marquardt algorithm for nonlinear least squares problems, where the Jacobian matrices are approximated via orthogonal spherical smoothing. It is shown that the gradient models which use the approximate Jacobian matrices are probabilistically first-order accurate. The high probability complexity bound of the algorithm is also given.

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来源期刊

Journal of Scientific Computing 数学-应用数学

CiteScore

4.00

自引率

12.00%

发文量

302

审稿时长

4-8 weeks

期刊介绍： Journal of Scientific Computing is an international interdisciplinary forum for the publication of papers on state-of-the-art developments in scientific computing and its applications in science and engineering. The journal publishes high-quality, peer-reviewed original papers, review papers and short communications on scientific computing.