Solving the system of nonsingular tensor equations via randomized Kaczmarz-like method
A great deal of attention has been paid to solve the system of tensor equations in recent years for its applications in various fields. In this paper, the Kaczmarz-like method, which is an effective approach for solving linear equations, is considered to deal with the system of tensor equations with...
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| Veröffentlicht in: | Journal of computational and applied mathematics Jg. 421; S. 114856 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Elsevier B.V
15.03.2023
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| ISSN: | 0377-0427, 1879-1778 |
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| Abstract | A great deal of attention has been paid to solve the system of tensor equations in recent years for its applications in various fields. In this paper, the Kaczmarz-like method, which is an effective approach for solving linear equations, is considered to deal with the system of tensor equations with nonsingular coefficient tensors. To reach this goal, two algorithms, i.e., the randomized Kaczmarz-like algorithm and its relaxed version, are proposed. The convergence analysis of these two approaches are given based on matrix SVD and the local tangential cone condition. Moreover, we present estimations of the convergence rate. Several numerical examples are presented to validate the theoretical results and reliability as well as effectiveness. |
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| AbstractList | A great deal of attention has been paid to solve the system of tensor equations in recent years for its applications in various fields. In this paper, the Kaczmarz-like method, which is an effective approach for solving linear equations, is considered to deal with the system of tensor equations with nonsingular coefficient tensors. To reach this goal, two algorithms, i.e., the randomized Kaczmarz-like algorithm and its relaxed version, are proposed. The convergence analysis of these two approaches are given based on matrix SVD and the local tangential cone condition. Moreover, we present estimations of the convergence rate. Several numerical examples are presented to validate the theoretical results and reliability as well as effectiveness. |
| ArticleNumber | 114856 |
| Author | Che, Maolin Wang, Xuezhong Wei, Yimin Mo, Changxin |
| Author_xml | – sequence: 1 givenname: Xuezhong surname: Wang fullname: Wang, Xuezhong email: xuezhongwang77@126.com organization: School of Mathematics and Statistics, Hexi University, Zhangye, 734000, PR China – sequence: 2 givenname: Maolin surname: Che fullname: Che, Maolin email: cheml@swufe.edu.cn organization: School of Mathematics, Southwest University of Finance and Economics, Chengdu, 611130, PR China – sequence: 3 givenname: Changxin surname: Mo fullname: Mo, Changxin email: cxmo16@cqnu.edu.cn organization: School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, PR China – sequence: 4 givenname: Yimin orcidid: 0000-0001-6192-0546 surname: Wei fullname: Wei, Yimin email: ymwei@fudan.edu.cn organization: School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, 200433, PR China |
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| Title | Solving the system of nonsingular tensor equations via randomized Kaczmarz-like method |
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