求解第一类Fredholm积分方程的一种新的正则化算法

摘要

应用一种新的正则化方法建立了一类新的求解第一类Fredholm积分方程的正则化算法,并借助Matlab软件给出了数值算例.数值结果与理论分析基本一致,而且表明文中建立的正则化比通常的Tikhonov正则化更精确.%Singular value system is applied to construct a new class of improved regularizing methods for solving the first kind of Fredholm integral equations with noisy data. By a priori choosing regularizing parameters, optimal convergence order of the regularized solution is obtained. And with aids of MATLAB software, numerical results are presented which roughly coincide with the theoretical analysis.