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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Zhenglang Ying,
  • Chenliang Li

摘要

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.