Abstract
A numerical method is proposed for estimating piecewise-constant solutions for Fredholm integral equations of the first kind. Two functionals, namely the weighted total variation (WTV) functional and the simplified Modica-Mortola (MM) functional, are introduced. The solution procedure consists of two stages. In the first stage, the WTV functional is minimized to obtain an approximate solution f TV * . In the second stage, the simplified MM functional is minimized to obtain the final result by using the damped Newton (DN) method with f TV * as the initial guess. The numerical implementation is given in detail, and numerical results of two examples are presented to illustrate the efficiency of the proposed approach.
Funder
National Natural Science Foundation of China
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference34 articles.
1. Discrete Inverse Problems: Insight and Algorithms;Hansen,2010
2. Computational Methods for Integral Equations;Delves,1985
3. Chebyshev finite difference method for Fredholm integro-differential equation;Dehghan;Int. J. Comput. Math.,2008
4. Numerical solution of linear Fredholm integral equations using sinecosine wavelets;Ghasemi;Int. J. Comput. Math.,2007
5. An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data;Koshev;CEJM,2013
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献