Wavelet Galerkin method for eigenvalue problem of a compact integral operator

We consider the approximation of eigenfunctions of a compact integral operator with a smooth kernel by the Galerkin method using wavelet bases. By truncating the Galerkin operator, we obtain a sparse representation of a matrix eigenvalue problem. We prove that the error bounds for the eigenvalues and for the distance between the spectral subspaces are of the orders O(nμ-2nr)O(nμ-2nr) and O(μ-nr)O(μ-nr), respectively, where μ−n denotes the norm of the partition and r   denotes the order of the wavelet basis functions. By iterating the eigenvectors, we show that the error bounds for the eigenvectors are of the order O(nμ-2nr)O(nμ-2nr). We illustrate our results with numerical results.