Tikhonov正则化
迭代函数
数学
正规化(语言学)
应用数学
反问题
趋同(经济学)
反向
理论(学习稳定性)
收敛速度
缩小
数学优化
数学分析
计算机科学
几何学
计算机网络
频道(广播)
人工智能
机器学习
经济
经济增长
作者
Gaurav Mittal,Ankik Kumar Giri
出处
期刊:Inverse Problems
[IOP Publishing]
日期:2022-10-13
卷期号:38 (12): 125008-125008
被引量:9
标识
DOI:10.1088/1361-6420/ac99fb
摘要
Abstract In this paper, we study the nonstationary iterated Tikhonov regularization method (NITRM) proposed by Jin and Zhong (2014 Numer. Math. 127 485–513) to solve the inverse problems, where the inverse mapping fulfills a Hölder stability estimate. The iterates of NITRM are defined through certain minimization problems in the settings of Banach spaces. In order to study the various important characteristics of the sought solution, we consider the non-smooth uniformly convex penalty terms in the minimization problems. In the case of noisy data, we terminate the method via a discrepancy principle and show the strong convergence of the iterates as well as the convergence with respect to the Bregman distance. For noise free data, we show the convergence of the iterates to the sought solution. Additionally, we derive the convergence rates of NITRM method for both the noisy and noise free data that are missing from the literature. In order to derive the convergence rates, we solely utilize the Hölder stability of the inverse mapping that opposes the standard analysis which requires a source condition as well as a nonlinearity estimate to be satisfied by the inverse mapping. Finally, we discuss three numerical examples to show the validity of our results.
科研通智能强力驱动
Strongly Powered by AbleSci AI