{"title":"Regularization operators versus regularization strategies","authors":"Thi-An Nguyen, C. Law","doi":"10.1515/jiip-2022-0073","DOIUrl":null,"url":null,"abstract":"Abstract In this note, we shall compare two important concepts of “regularization operators” and “regularization strategies” that appear in different classical monographs. The definition of a regularization operator is related to the Moore–Penrose inverse of the operator. In general, a regularization operator is a regularization strategy. We shall show that the converse is also true under some conditions. It is interesting to note that these two systems share analogous properties.","PeriodicalId":50171,"journal":{"name":"Journal of Inverse and Ill-Posed Problems","volume":"31 1","pages":"625 - 629"},"PeriodicalIF":1.0000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Inverse and Ill-Posed Problems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jiip-2022-0073","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract In this note, we shall compare two important concepts of “regularization operators” and “regularization strategies” that appear in different classical monographs. The definition of a regularization operator is related to the Moore–Penrose inverse of the operator. In general, a regularization operator is a regularization strategy. We shall show that the converse is also true under some conditions. It is interesting to note that these two systems share analogous properties.
期刊介绍：
This journal aims to present original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.
Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest.
The following topics are covered:
Inverse problems
existence and uniqueness theorems
stability estimates
optimization and identification problems
numerical methods
Ill-posed problems
regularization theory
operator equations
integral geometry
Applications
inverse problems in geophysics, electrodynamics and acoustics
inverse problems in ecology
inverse and ill-posed problems in medicine
mathematical problems of tomography
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