Preconditioned TBiCOR and TCORS algorithms for solving the Sylvester tensor equation

Guang-Xin Huang, Qi-Xing Chen and Feng Yin

Applied Mathematics and Computation, 2022, vol. 422, issue C

Abstract: In this paper, the preconditioned TBiCOR and TCORS methods are presented for solving the Sylvester tensor equation. A tensor Lanczos L-Biorthogonalization algorithm (TLB) is derived for solving the Sylvester tensor equation. Two improved TLB methods are presented. One is the biconjugate L-orthogonal residual algorithm in tensor form (TBiCOR), which implements the LU decomposition for the triangular coefficient matrix derived by the TLB method. The other is the conjugate L-orthogonal residual squared algorithm in tensor form (TCORS), which introduces a square operator to the residual of the TBiCOR algorithm. A preconditioner based on the nearest Kronecker product is used to accelerate the TBiCOR and TCORS algorithms, and we obtain the preconditioned TBiCOR algorithm (PTBiCOR) and preconditioned TCORS algorithm (PTCORS). The proposed algorithms are proved to be convergent within finite steps of iteration without roundoff errors. Several examples illustrate that the preconditioned TBiCOR and TCORS algorithms present excellent convergence.

Keywords: TLB; TBiCOR; TCORS; Sylvester tensor equation; Preconditioner (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:422:y:2022:i:c:s0096300322000704

DOI: 10.1016/j.amc.2022.126984

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