About the Tikhonov Regularization Method for the Solution of Incorrect Problems

Q3 Mathematics

WSEAS Transactions on Systems and Control Pub Date : 2023-06-28 DOI:10.37394/23202.2023.22.66

V. Ryabov, I. Burova

引用次数: 0

Abstract

From time to time, papers are published containing gross errors when solving integral equations of the first kind. This paper is devoted to the analysis of these errors. The paper considers Tikhonov’s weak and operator regularization. To construct a solution to the integral equation, the local splines of the Lagrangian type of the second order of approximation, as well as the local splines of the Hermitian type of the fourth order of approximation of the first level, are used. The results of numerical experiments are presented.

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关于不正确问题求解的吉洪诺夫正则化方法

有时，发表的论文在求解第一类积分方程时包含严重的错误。本文致力于对这些错误进行分析。本文考虑了Tikhonov的弱正则化和算子正则化。为了构造积分方程的解，使用了二阶近似的拉格朗日型局部样条和一阶近似的四阶厄密型局部样条。给出了数值实验结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

WSEAS Transactions on Systems and Control Mathematics-Control and Optimization

CiteScore

1.80

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Systems and Control publishes original research papers relating to systems theory and automatic control. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with systems theory, dynamical systems, linear and non-linear control, intelligent control, robotics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.