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Developing iterative algorithms to solve Sylvester tensor equations
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DOI：10.1016/j.amc.2021.126403.png)
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Abstract
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This paper is concerned with solving high order Sylvester tensor equation arising in con-trol theory. We propose the tensor forms of the bi-conjugate gradient and bi-conjugate residual methods for solving the tensor equation. To improve their performance, two pre-conditioned iterative algorithms based on the nearest Kronecker product are developed for finding its solution. We also prove that the proposed algorithms are convergent to an exact solution within finite iteration steps for any initial tensor in the absence of round-off er -rors. At last, some numerical examples are provided to illustrate the feasibility and validity of the algorithms proposed. (c) 2021 Elsevier Inc. All rights reserved.
Keywords:
Sylvester tensor equation
Bi-conjugate gradient
Bi-conjugate residual
Tensor forms
Nearest Kronecker product
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