On RGI Algorithms for Solving Sylvester Tensor Equations

IF 0.6 4区 数学 Q3 MATHEMATICS
Xin-Fang Zhang, Qingwen Wang
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引用次数: 4

Abstract

. This paper is concerned with studying the relaxed gradient-based iterative method based on tensor format to solve the Sylvester tensor equation. From the information given by the previous steps, we further develop a modified relaxed gradient-based iterative method which converges faster than the method above. Under some suitable conditions, we prove that the introduced methods are convergent to the unique solution for any initial tensor. At last, we provide some numerical examples to show that our methods perform much better than the GI algorithm proposed by Chen and Lu (Math. Probl. Eng. 2013) both in the number of iteration steps and the elapsed CPU time.
求解Sylvester张量方程的RGI算法
本文研究了基于张量格式的基于松弛梯度的迭代方法来求解Sylvester张量方程。根据前面步骤提供的信息,我们进一步开发了一种改进的基于松弛梯度的迭代方法,该方法比上面的方法收敛更快。在一些适当的条件下,我们证明了所引入的方法收敛于任何初始张量的唯一解。最后,我们提供了一些数值例子,表明我们的方法在迭代步数和CPU运行时间方面都比Chen和Lu(Math.Probl.Eng.2013)提出的GI算法要好得多。
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
CiteScore
1.10
自引率
0.00%
发文量
35
审稿时长
3 months
期刊介绍: The Taiwanese Journal of Mathematics, published by the Mathematical Society of the Republic of China (Taiwan), is a continuation of the former Chinese Journal of Mathematics (1973-1996). It aims to publish original research papers and survey articles in all areas of mathematics. It will also occasionally publish proceedings of conferences co-organized by the Society. The purpose is to reflect the progress of the mathematical research in Taiwan and, by providing an international forum, to stimulate its further developments. The journal appears bimonthly each year beginning from 2008.
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