{"title":"About the Tikhonov Regularization Method for the Solution of Incorrect Problems","authors":"V. Ryabov, I. Burova","doi":"10.37394/23202.2023.22.66","DOIUrl":null,"url":null,"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.","PeriodicalId":39422,"journal":{"name":"WSEAS Transactions on Systems and Control","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS Transactions on Systems and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/23202.2023.22.66","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
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.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
