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Tensor product-type methods for solving Sylvester tensor equations

Author

Listed:
  • Niu, Jing
  • Sogabe, Tomohiro
  • Du, Lei
  • Kemmochi, Tomoya
  • Zhang, Shao-Liang

Abstract

The tensor biconjugate gradient (TBiCG) method has recently been proposed for solving Sylvester tensor equations. The TBiCG method is based on the BiCG method that may exhibit irregular convergence behavior. To overcome the limitations, product-type methods, such as BiCGSTAB and GPBiCG, have been proposed. In this study, we apply the idea of product-type methods to solve Sylvester tensor equations and propose tensor GPBiCG and BiCGSTAB methods. Furthermore, we consider preconditioned algorithms of the tensor GPBiCG and BiCGSTAB methods using the nearest Kronecker product preconditioner. Numerical experiments illustrate that the proposed methods are competitive with some existing methods.

Suggested Citation

  • Niu, Jing & Sogabe, Tomohiro & Du, Lei & Kemmochi, Tomoya & Zhang, Shao-Liang, 2023. "Tensor product-type methods for solving Sylvester tensor equations," Applied Mathematics and Computation, Elsevier, vol. 457(C).
    • Handle: RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003247
    DOI: 10.1016/j.amc.2023.128155
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