Multiscale Projection Iterative Algorithm For Solving The First Kind Of Integral Equations

One is to solve the first kind of linear integral equation by using the compressed multiscale projection method.The second is to solve the first class of nonlinear integral equations by using multiscale projection discretization method.In chapter 1,the basic concepts and classification of integral equations are introduced,and then the research progress of solving the first kind of linear integral equations and the first kind of nonlinear integral equations is reviewed.Chapter 2 studies the compressed projection iterative scheme for solving the first kind of linear integral equation in real Hilbert space.By combining the compressed multiscale projection method with the Landweber iterative method,the convergence results and the convergence speed estimation results of the approximate solution of the compressed projection iterative scheme are obtained.Chapter 3 studies the projection iterative scheme for solving the first kind of nonlinear integral equations in real Hilbert space.By combining the multiscale Galerkin projection method with the improved Landweber iterative method,the convergence rate estimation results of the approximate solution of the improved projection iterative scheme are obtained.Chapter 4 summarizes the main work of this paper,and puts forward the relevant research questions.