求解半正定病态积分方程的多尺度快速Lavrentiev迭代算法

A Fast Lavrentiev Iterative Methods for Solving the Semi-definite Ill-posed Integral Equation Based on the Truncated Projection Method

基于多尺度投影方法,构造了求解半正定病态积分方程的截断快速Lavrentiev迭代算法,并给出了新的后验参数选择办法.与传统全投影方法相比,减少了内积计算个数,保持了最优收敛率.最后,算例验证了算法的有效性.

In this paper,a fast iterative Lavrentiev method is established for so lving the semi-definite ill-posed integral equation based on the optimization of projection method,and a posteriori parameter choice strategy of improvement is proposed.Compared with the traditional projection technique,we keep the optima l convergence rate,but less than the number of inner products caculation.Finall y,numerical experiments are given to illustrate the efficiency of the method.