求解隐式迭代方程的多尺度配置法

Multiscale collocation method for solving implicit iterative equations

用多尺度快速配置法求解病态积分方程的隐式迭代方程.在积分算子是扇形紧算子时,该方法得到了离散隐式迭代方程的近似解.采用Morozov偏差原理作为停止准则,并证明了在该准则下隐式迭代正则化方法所得近似解的收敛率.最后,用数值实验证实理论结果和说明数值方法的有效性.

In the paper,the implicit iterative equation of the ill-posed integral equation is solved by the fast multiscale collocation method.When the integral operator is the sector compact operator,this method obtains the approximate solutions of the discrete implicit iterative equations.The convergence rate of the approximate solution obtained by the implicit iterative regularization method is proved by using the Morozov deviation principle as the stopping criterion.Finally,numerical experiments are presented to confirm the theoretical results and illustrate the efficiency of the method.