不适定问题和共轭梯度法：存在离散化和建模误差时的最优收敛速度

IF 0.9 4区数学 Q2 MATHEMATICS

Journal of Inverse and Ill-Posed Problems Pub Date : 2022-11-08 DOI:10.1515/jiip-2022-0039

A. Neubauer

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引用次数: 0

摘要

摘要在本文中，我们证明了共轭梯度法应用于线性不适定问题的阶最优收敛速度，不仅当数据有噪声时，而且当算子受到离散化和建模误差的扰动时。

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Ill-posed problems and the conjugate gradient method: Optimal convergence rates in the presence of discretization and modelling errors

Abstract In this paper, we prove order-optimal convergence rates for the conjugate gradient method applied to linear ill-posed problems when not only the data are noisy but also when the operator is perturbed via discretization and modelling errors.

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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