Iterated fast multiscale Galerkin methods for eigen-problems of compact integral operators

An iterated fast multiscale Galerkin method is developed for solving the eigen-problem of integral operators with weakly singular kernels. We propose a theoretical framework for analysis of the convergence of these methods and show the fast multiscale Galerkin method obtain the optimal convergence order for eigenvectors and superconvergence order for eigenvalues while the computational complexity for coefficient matrix is almost optimal. The iterated fast multiscale Galerkin method can improve the convergence for eigenvectors and exhibit superconvergence through the iteration technique. Numerical examples are presented to illustrate the theoretical estimates for the error of these methods.