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June, 2022 On RGI Algorithms for Solving Sylvester Tensor Equations
Xin-Fang Zhang, Qing-Wen Wang
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Taiwanese J. Math. 26(3): 501-519 (June, 2022). DOI: 10.11650/tjm/220103

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.

Funding Statement

This research was supported by National Natural Science Foundation of China [grant number 11971294].

Citation

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Xin-Fang Zhang. Qing-Wen Wang. "On RGI Algorithms for Solving Sylvester Tensor Equations." Taiwanese J. Math. 26 (3) 501 - 519, June, 2022. https://doi.org/10.11650/tjm/220103

Information

Received: 2 February 2021; Revised: 13 November 2021; Accepted: 16 January 2022; Published: June, 2022
First available in Project Euclid: 14 February 2022

Digital Object Identifier: 10.11650/tjm/220103

Subjects:
Primary: 15A69 , 65F10

Keywords: modified relaxed gradient-based iterative method , relaxed gradient-based iterative method , Sylvester tensor equation , tensor format

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

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Vol.26 • No. 3 • June, 2022
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