On convergence of a sketch-and-project method for the matrix equation $$AXB=C$$

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-07-12 DOI:10.1007/s40314-024-02847-8

Wendi Bao, Zhiwei Guo, Weiguo Li, Ying Lv

引用次数: 0

Abstract

In this paper, based on Lagrangian functions of the optimization problem we develop a sketch-and-project method for solving the linear matrix equation $AXB = C$ by introducing three parameters. A thorough convergence analysis on the proposed method is explored in details. A lower bound on the convergence rate and some convergence conditions are derived. By varying three parameters in the new method and convergence theorems, an array of well-known algorithms and their convergence results are recovered. Finally, numerical experiments are given to illustrate the effectiveness of recovered methods.

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论矩阵方程 $$AXB=C$$ 的草图与项目方法的收敛性

本文以优化问题的拉格朗日函数为基础，通过引入三个参数，开发了一种求解线性矩阵方程 $AXB = C$ 的草图-项目方法。我们详细探讨了所提方法的收敛性分析。得出了收敛率下限和一些收敛条件。通过改变新方法中的三个参数和收敛定理，恢复了一系列著名算法及其收敛结果。最后，给出了数值实验来说明恢复方法的有效性。

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

Computational and Applied Mathematics MATHEMATICS, APPLIED-

自引率

11.50%

发文量

352

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.