Implicit iterative scheme based on the pseudo--inversion algorithm and its application

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Abstract

A new version of the implicit iterative scheme is proposed for the implementation of which only matrix-vector computational procedures are required. This makes the proposed computational scheme potentially highly efficient for solving a wide class of high-dimensional problems on modern high-performance computing platforms, such as Nvidia Cuda. It is shown that the proposed algorithms can be used to solve ill-conditioned linear systems and least squares problems, as well as to construct iterative regularization algorithms. The results of computational experiments are presented, confirming the effectiveness of the proposed computational algorithms.

About the authors

Alexandr I. Zhdanov

Samara State Technical University; Samara State Technical University, Novokuybyshevsk Branch

Author for correspondence.
Email: zhdanovaleksan@yandex.ru
ORCID iD: 0000-0001-6082-9097
https://www.mathnet.ru/person41724

Dr. Phys. & Math. Sci., Professor; Professor; Dept. of Applied Mathematics and
Informatics; Professor; Dept. of Electrical Power Engineering, Electrical Engineering, and Automation Process Technology

Russian Federation, 443100, Samara, Molodogvardeyskaya st., 244; 446200, Novokuybyshevsk, Mironova st., 5

Yuri V. Sidorov

Samara State Technical University

Email: linuxboy2007@gmail.com
ORCID iD: 0000-0002-8138-9200
https://www.mathnet.ru/person114787

Cand. Phys. & Math. Sci.; Associate Professor; Dept. of Applied Mathematics and Informatics

Russian Federation, 443100, Samara, Molodogvardeyskaya st., 244

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2. Figure 1. Convergence rate of the iterative algorithm (10) when solving ill-conditioned systems of linear equations (1)

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3. Figure 2. Convergence rate of the iterative process when solving the perturbed problem (13); the horizontal line corresponds to the value $\tau \delta$

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