求解Richardson迭代方程的快速配置法

FAST COLLOCATION METHODS FOR SOLVING RICHARDSON ITERATION

本文依据多尺度快速配置法求解第一类Fredholm积分方程的Richardson迭代正则化方程.该方法得到了离散Richardson迭代正则化方程的快速解,在积分算子是弱扇形紧算子时,利用改进的迭代停止准则,给出了Richardson迭代正则化方法所得近似解的收敛率.最后,数值例子说明了算法的有效性.

In this paper we develop a fast multiscale collocation method solving ill-posed Fredholm integral equation of the first kind via Richardson iteration. The method leads to fast solutions of discrete Richardson iteration regularization, if the integral operator is the weakly sectorial operator, the convergence rates of the Richardson iteration regularization are achieved by using a modified iterative stop rule. Finally, numerical experiments are given to illustrate the efficiency of the method.