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Journal Articles Journal of Computational and Applied Mathematics Year : 2020

On global iterative schemes based on Hessenberg process for (ill-posed) Sylvester tensor equations

Mehdi Najafi-Kalyani
  • Function : Author
Fatemeh Panjeh Ali Beik

Abstract

This paper is concerned with studying the performance of some global iterative schemes based on Hessenberg process to solve the Sylvester tensor equation (STE). Furthermore, we briefly mention the implementation of flexible versions. Under certain conditions, we devote part of the work to derive upper bounds for condition number of matrices with a special Kronecker product structure which can be helpful to obtain error bounds related to perturbation analysis of the mentioned STE. In addition, we propose using the Tikhonov regularization technique in conjunction with the tensor form of the flexible Hessenberg process when the STE is ill-posed. Numerical examples are examined for two test problems arising from discretization of three-dimensional partial differential equations. We also present some experimental results related to restoration of color images.
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Dates and versions

hal-04413541 , version 1 (23-01-2024)

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Mehdi Najafi-Kalyani, Fatemeh Panjeh Ali Beik, Khalide Jbilou. On global iterative schemes based on Hessenberg process for (ill-posed) Sylvester tensor equations. Journal of Computational and Applied Mathematics, 2020, 373, pp.112216. ⟨10.1016/j.cam.2019.03.045⟩. ⟨hal-04413541⟩
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