Conjugate gradient algorithm for consistent generalized Sylvester-transpose matrix equations

Kanjanaporn Tansri; Sarawanee Choomklang; Pattrawut Chansangiam; Kanjanaporn Tansri; Sarawanee Choomklang; Pattrawut Chansangiam

doi:10.3934/math.2022299

AIMS Mathematics

2022, Volume 7, Issue 4: 5386-5407. doi: 10.3934/math.2022299

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Research article

Conjugate gradient algorithm for consistent generalized Sylvester-transpose matrix equations

Department of Mathematics, School of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, Thailand

Received: 26 October 2021 Revised: 13 December 2021 Accepted: 21 December 2021 Published: 06 January 2022
MSC : 15A60, 15A69, 65F45

We develop an effective algorithm to find a well-approximate solution of a generalized Sylvester-transpose matrix equation where all coefficient matrices and an unknown matrix are rectangular. The algorithm aims to construct a finite sequence of approximated solutions from any given initial matrix. It turns out that the associated residual matrices are orthogonal, and thus, the desire solution comes out in the final step with a satisfactory error. We provide numerical experiments to show the capability and performance of the algorithm.
- conjugate gradient agorithm,
- generalized Sylvester-transpose matrix equation,
- Kronecker product,
- matrix norm,
- orthogonality
Citation: Kanjanaporn Tansri, Sarawanee Choomklang, Pattrawut Chansangiam. Conjugate gradient algorithm for consistent generalized Sylvester-transpose matrix equations[J]. AIMS Mathematics, 2022, 7(4): 5386-5407. doi: 10.3934/math.2022299

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Abstract

We develop an effective algorithm to find a well-approximate solution of a generalized Sylvester-transpose matrix equation where all coefficient matrices and an unknown matrix are rectangular. The algorithm aims to construct a finite sequence of approximated solutions from any given initial matrix. It turns out that the associated residual matrices are orthogonal, and thus, the desire solution comes out in the final step with a satisfactory error. We provide numerical experiments to show the capability and performance of the algorithm.

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