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Original scientific paper

An optimality property of an approximated solution computed by the Hessenberg method

Mehdi Najafi-Kalyani orcid id orcid.org/0000-0003-2474-6096 ; Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
Fatemeh P. A. Beik ; Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran


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Abstract

We revisit the implementation of the Krylov subspace method based on the Hessenberg process for general linear operator equations. It is established that at each step, the computed approximate solution can be regarded by the corresponding approach as the minimizer of a certain norm of residual corresponding to the obtained approximate solution of the system. Test problems are numerically examined for solving tensor equations with a cosine transform product arising from image restoration to compare the performance of the Krylov subspace methods in conjunction with the Tikhonov regularization technique based on Hessenberg and Arnoldi processes.

Keywords

Krylov subspace method, tensor equation, Tikhonov regularization, cosine transform product, Hessenberg process, Arnoldi process, image processing

Hrčak ID:

285132

URI

https://hrcak.srce.hr/285132

Publication date:

13.11.2022.

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