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Anderson acceleration of the tensor relaxation Jacobi method for solving Sylvester tensor equations.

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Title: Anderson acceleration of the tensor relaxation Jacobi method for solving Sylvester tensor equations.
Authors: Ying, Zhenglang1 (AUTHOR) zhenglying@126.com, Li, Chenliang1 (AUTHOR) chenli@guet.edu.cn
Source: Calcolo. Nov2025, Vol. 62 Issue 4, p1-21. 21p.
Subjects: Jacobi method, Sylvester matrix equations, Calculus of tensors, Iterative methods (Mathematics), Computational complexity, Anderson, Jonathan, 1984-, Empirical research, Partial differential equations, Extrapolation
Abstract: For the Sylvester tensor equations which arise from high-dimensional partial differential equation problems, firstly, a relaxation Jacobi iterative method based on the tensor format is constructed, and it has less computational complexity compared with the classical relaxation Jacobi method with a matrix–vector structure. Then, based on Anderson extrapolation, Anderson acceleration of the tensor relaxation Jacobi iterative method is proposed. Moreover, the convergence of these methods is given. Finally, the effectiveness of the new methods is verified by some numerical examples. [ABSTRACT FROM AUTHOR]
Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 188855221
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Anderson acceleration of the tensor relaxation Jacobi method for solving Sylvester tensor equations.
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  Data: <searchLink fieldCode="AR" term="%22Ying%2C+Zhenglang%22">Ying, Zhenglang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhenglying@126.com</i><br /><searchLink fieldCode="AR" term="%22Li%2C+Chenliang%22">Li, Chenliang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> chenli@guet.edu.cn</i>
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  Data: <searchLink fieldCode="DE" term="%22Jacobi+method%22">Jacobi method</searchLink><br /><searchLink fieldCode="DE" term="%22Sylvester+matrix+equations%22">Sylvester matrix equations</searchLink><br /><searchLink fieldCode="DE" term="%22Calculus+of+tensors%22">Calculus of tensors</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink><br /><searchLink fieldCode="DE" term="%22Anderson%2C+Jonathan%2C+1984-%22">Anderson, Jonathan, 1984-</searchLink><br /><searchLink fieldCode="DE" term="%22Empirical+research%22">Empirical research</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Extrapolation%22">Extrapolation</searchLink>
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  Data: For the Sylvester tensor equations which arise from high-dimensional partial differential equation problems, firstly, a relaxation Jacobi iterative method based on the tensor format is constructed, and it has less computational complexity compared with the classical relaxation Jacobi method with a matrix–vector structure. Then, based on Anderson extrapolation, Anderson acceleration of the tensor relaxation Jacobi iterative method is proposed. Moreover, the convergence of these methods is given. Finally, the effectiveness of the new methods is verified by some numerical examples. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Calcolo is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1007/s10092-025-00659-8
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 21
        StartPage: 1
    Subjects:
      – SubjectFull: Jacobi method
        Type: general
      – SubjectFull: Sylvester matrix equations
        Type: general
      – SubjectFull: Calculus of tensors
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: Computational complexity
        Type: general
      – SubjectFull: Anderson, Jonathan, 1984-
        Type: general
      – SubjectFull: Empirical research
        Type: general
      – SubjectFull: Partial differential equations
        Type: general
      – SubjectFull: Extrapolation
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      – TitleFull: Anderson acceleration of the tensor relaxation Jacobi method for solving Sylvester tensor equations.
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            – D: 01
              M: 11
              Text: Nov2025
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              Y: 2025
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