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

Mathematical Communications

article

Mehdi Najafi-Kalyani¹  Fatemeh P. A. Beik¹ 

[1] Department of Mathematics, Vali-e-Asr University of Rafsanjan

关键词: Krylov subspace method;    tensor equation;    Tikhonov regularization;    cosine transform product;    Hessenberg process;    Arnoldi process;    image processing;   

学科分类：工程和技术（综合）

来源: Sveuciliste Josipa Jurja Strossmayera u Osijeku * Odjel za Matematiku / University of Osijek, Department of Mathematics

【 摘 要 】

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.

【 授权许可】

CC BY-NC-ND