The First Kind Of Pathological Integral Equation Multiscale Projection Algorithm Quickly

In this paper, we consider numerically solving fredholm integral equation of the first kind byapplying fast multiscale Galerkin method. This paper is organized as follows：In section1, weanalyse the study present situation at home and abroad. In section2, we develop a fast multiscaleprojection method to solve the discretization of the DSM problem,Compared with the traditionalprojection technique, we keep the optimal convergence rate, but less than the number of innerproducts calculation. Finally, numerical experiments are given to illustrate the efficiency of themethod.In section3, a fast iterative Lavrentiev method is established for solving the semi-definiteill-posed integral equation based on the optimization of projection method, and a posterioriparameter choice strategies of improvement is proposed，Compared with the traditional projectiontechnique, we keep the optimal convergence rate, but less than the number of inner productscaculation. Finally, numerical experiments are given to illustrate the efficiency of the method.