Regularization operators versus regularization strategies

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2023-06-01 DOI:10.1515/jiip-2022-0073

Thi-An Nguyen, C. Law

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.

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正则化操作符与正则化策略

在本文中，我们将比较不同经典专著中出现的“正则化算子”和“正则化策略”两个重要概念。正则化算子的定义与算子的摩尔-彭罗斯逆有关。一般来说，正则化算子是一种正则化策略。我们将证明，在某些条件下，反过来也是成立的。有趣的是，这两个系统具有相似的性质。

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

Journal of Inverse and Ill-Posed Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

9.10%

发文量

审稿时长

>12 weeks

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