Hilbert空间中非线性逆问题的迭代正则化简化Landweber迭代研究

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

Numerical Functional Analysis and Optimization Pub Date : 2023-04-21 DOI:10.1080/01630563.2023.2183510

S. K. Dixit

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引用次数: 0

摘要

摘要Lanweber型方法是求解线性和非线性不适定问题的一种著名的正则化方法。在本文中，我们考虑了Landweber方法的一种简化形式，即求解非线性不适定问题的迭代正则化简化Landweber迭代。我们研究了该方法在标准条件下的非线性收敛性分析以及在Hölder型源条件下的收敛速度。最后，通过数值模拟验证了该方法的有效性。

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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A Study of an Iteratively-Regularized Simplified Landweber Iteration for Nonlinear Inverse Problems in Hilbert Spaces

Abstract Lanweber-type methods are a well-known regularization methods to solve linear and nonlinear ill-posed problems. In this article, we consider a simplified form of Landweber method, say, an iteratively-regularized simplified Landweber iteration for solving nonlinear ill-posed problems. We study a detailed convergence analysis of the method under standard conditions on the nonlinearity and the rate of convergence under a Hölder-type source condition. Finally, numerical simulations are performed to validate the performance of the method.

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来源期刊

Numerical Functional Analysis and Optimization 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal. Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.