求解张量方程的草图-投影法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-09-19 DOI:10.1016/j.amc.2025.129735

Ling Tang , Yanjun Zhang , Hanyu Li

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引用次数: 0

摘要

我们提出了一种基于t积的求解线性张量方程的常规草图-投影方法，并给出了其等效的傅里叶域版本，以及与现有经典矩阵方程方法相对应的几个特殊情况。此外，我们通过一个层次方法扩展这个框架来求解广义Sylvester张量方程。所有方法在期望上都是线性收敛的。最后，通过数值实验验证了该方法的有效性。

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On sketch-and-project methods for solving tensor equations

We propose a regular sketch-and-project method for solving linear tensor equations based on the t-product and present its equivalent Fourier domain version, along with several special cases corresponding to existing classical matrix equation methods. Furthermore, we extend this framework via a hierarchical approach to solve generalized Sylvester tensor equations. All the methods are proved to converge linearly in expectation. Finally, numerical experiments demonstrate the efficiency and effectiveness of the proposed approach.

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.