A Two-Stage Method for Piecewise-Constant Solution for Fredholm Integral Equations of the First Kind

作者：Lin, Fu-Rong^*; Yang, Shi-Wei

来源：Mathematics, 2017, 5(2): 28.

DOI：10.3390/math5020028

• Fredholm integral equation of the first kind
• regularization
• piecewise-constant solution
• total variation (TV) functional
• Modica-Mortola (MM) functional

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.

• 出版日期2017-6
• 单位汕头大学