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

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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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The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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  1. Department of Mathematics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, Iran

    Eisa Khosravi Dehdezi

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Dehdezi, E.K. HOBi-CGSTAB and HOBi-CRSTAB methods for solving some tensor equations. Afr. Mat. 35, 14 (2024). https://doi.org/10.1007/s13370-023-01155-4

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