Spectral approximation using iterated discrete Galerkin method

We consider approximation of eigenelements of an integral operator with a smooth kernel by discrete Galerkin and iterated discrete Galerkin methods. We prove that by using a sufficiently accurate numerical quadrature formula, the orders of convergence in Galerkin/iterated Galerkin methods are preserved. We show that we achieve the same order of convergence in iterated discrete Galerkin method as in Nystrom method, but the size of the generalised eigenvalue problem to be solved is reduced by half