无界矩阵算子的稳定近似求值及其在逆问题中的应用

IF 2.1 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2025-05-09 DOI:10.1007/s10444-025-10235-x

Shuang Yu, Hongqi Yang

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引用次数: 0

摘要

引入了一种双参数Tikhonov正则化方法来逼近具有无界矩阵算子的病态问题。导出了该问题正则解的存在唯一性。采用先验和后验参数选择策略，对正则化解进行收敛性分析。作为应用，我们将正则化方法应用于热传导方程源项和初值问题的同时反演，并通过数值实验验证了该方法的有效性。

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Stable approximate evaluation of unbounded matrix operator and its application to an inverse problem

We introduce a two-parameter Tikhonov regularization method to approximate an ill-posed problem with an unbounded matrix operator. The existence and uniqueness of regularized solutions to the problem are derived. With an a priori as well as an a posteriori parameter choice strategy, convergence analysis of the regularized solution is presented. As an application, we apply the regularization to a simultaneous inversion of the source term and the initial value problem for a heat conduction equation, and numerical experiments are given to demonstrate the effectiveness of the proposed method.

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来源期刊

Advances in Computational Mathematics 数学-应用数学

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.