求解矩阵多项式方程的两种全局拟牛顿算法

IF 2.5 3区数学 Q1 MATHEMATICS, APPLIED

Computational & Applied Mathematics Pub Date : 2023-09-20 DOI:10.1007/s40314-023-02450-3

Mauricio Macías, Rosana Pérez, Héctor Jairo Martínez

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引用次数: 0

摘要

本文将Macías等人提出的拟牛顿算法(appll Math compuput 441:127678, 2023)进行了全局化，引入了精确线搜索，给出了价值函数的多项式逼近，并推导了其最小区间的充分条件。利用精确价值函数及其近似，提出了求解矩阵多项式方程的两种全局拟牛顿算法。对于每一种算法，我们都证明了精确线搜索不影响拟牛顿法的收敛性。此外，我们还提出了算法建议的比较数值测试，其中我们还与全局牛顿方法进行了比较。

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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Two global quasi-Newton algorithms for solving matrix polynomial equations

Abstract In this article, we globalize the quasi-Newton algorithm proposed in Macías et al. (Appl Math Comput 441:127678, 2023) introducing an exact line search, we propose a polynomial approximation to the merit function and we deduce a sufficient condition for its minimization interval. We use the exact merit function and its approximation to propose two global quasi-Newton algorithms for solving matrix polynomial equations. For each algorithm, we prove that the exact line search does not affect the convergence of quasi-Newton method. In addition, we present comparative numerical tests of the algorithmic proposals in which we also compare with global Newton’s method.

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来源期刊

Computational & Applied Mathematics Mathematics-Computational Mathematics

CiteScore

4.50

自引率

11.50%

发文量

352

审稿时长

>12 weeks

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.