HOBi-CGSTAB and HOBi-CRSTAB methods for solving some tensor equations

IF 0.9 Q2 MATHEMATICS Afrika Matematika Pub Date : 2023-12-12 DOI:10.1007/s13370-023-01155-4

Eisa Khosravi Dehdezi

引用次数: 0

Abstract

Recently, solving tensor equations (or multilinear systems) has attracted a lot of attention. This paper investigates the tensor form of the Bi-CGSTAB and Bi-CRSTAB methods, by employing Kronecker product, vectorization, and bilinear operator, to solve the generalized coupled Sylvester tensor equations \(\sum _{i=1}^{n}({\mathcal {X}}\times _1A_{i1}\times _2A_{i2}+\mathcal Y\times _1B_{i1}\times _2B_{i2})={\mathcal {E}}_1,~\sum _{i=1}^{n}(\mathcal X\times _1C_{i1}\times _2C_{i2}+\mathcal Y\times _1D_{i1}\times _2D_{i2})={\mathcal {E}}_2,\) with no matricization. Also some properties of the new methods are presented. By applying multilinear operator, the proposed methods are extended to the general form. Some numerical examples are provided to compare the efficiency of the investigated methods with some existing popular algorithms. Finally, some concluding remarks are given.

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求解某些张量方程的 HOBi-CGSTAB 和 HOBi-CRSTAB 方法

最近，张量方程（或多线性系统）的求解引起了广泛关注。本文通过使用 Kronecker 积、矢量化和双线性算子，研究了 Bi-CGSTAB 和 Bi-CRSTAB 方法的张量形式、来求解广义耦合西尔维斯特张量方程 \(\sum _{i=1}^{n}({\mathcal {X}}\times _1A_{i1}\times _2A_{i2}+\mathcal Y\times _1B_{i1}\times _2B_{i2})={\mathcal {E}}_1、~sum _{i=1}^{n}(\mathcal X\times _1C_{i1}\times _2C_{i2}+\mathcal Y\times _1D_{i1}\times _2D_{i2})={\mathcal {E}}_2,\) 没有矩阵化。此外，还介绍了新方法的一些特性。通过应用多线性算子，提出的方法被扩展到一般形式。还提供了一些数值示例，以比较所研究方法与一些现有流行算法的效率。最后，给出了一些结束语。

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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