Developing iterative algorithms to solve Sylvester tensor equations
Developing iterative algorithms to solve Sylvester tensor equations
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DOI：
10.1016/j.amc.2021.126403
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发表时间：
2021-11
期刊：
影响因子：
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通讯作者：
Xin-Fang Zhang;Qingwen Wang
中科院分区：
文献类型：
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作者：
Xin-Fang Zhang;Qingwen Wang
本文研究控制论中高阶西尔维斯特张量方程的求解问题。给出了求解张量方程的双共轭梯度法和双共轭残量法的张量形式。为了提高其性能，提出了两种基于最近Kronecker积的预条件迭代算法。我们还证明了所提出的算法收敛到一个精确的解决方案，在有限的迭代步骤中的任何初始张量的舍入误差的情况下。最后通过数值算例说明了算法的可行性和有效性。
This paper is concerned with solving high order Sylvester tensor equation arising in control 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 preconditioned 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 errors. At last, some numerical examples are provided to illustrate the feasibility and validity of the algorithms proposed.