Convergence rates of Tikhonov regularization for recovering growth rates in a Lotka-Volterra competition model with diffusion

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2021-01-01 DOI:10.3934/IPI.2021023

De-Han Chen, Daijun Jiang

引用次数: 3

Abstract

In this paper, we shall study the convergence rates of Tikhonov regularizations for the recovery of the growth rates in a Lotka-Volterra competition model with diffusion. The ill-posed inverse problem is transformed into a nonlinear minimization system by an appropriately selected version of Tikhonov regularization. The existence of the minimizers to the minimization system is demonstrated. We shall propose a new variational source condition, which will be rigorously verified under a Hölder type stability estimate. We will also derive the reasonable convergence rates under the new variational source condition.

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具有扩散的Lotka-Volterra竞争模型中恢复增长率的Tikhonov正则化收敛率

在本文中，我们将研究具有扩散的Lotka-Volterra竞争模型中增长率恢复的Tikhonov正则化收敛率。通过适当选择吉洪诺夫正则化，将病态逆问题转化为非线性最小化系统。证明了最小化系统的最小值存在性。我们将提出一个新的变分源条件，该条件将在Hölder型稳定性估计下进行严格验证。我们还将推导出在新的变分源条件下的合理收敛速率。

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

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.