Superconvergent Nyström and degenerate kernel methods for eigenvalue problems
The authors propose new superconvergent Nyström and degenerate kernel methods based on projections onto the space of discontinuous piecewise polynomials of degree \(\leq R - 1\) for the approximate solution of eigenvalue problems for compact integral operators. Similar to a method studied by \textit{R. P. Kulkarni}, [Math. Comput. 75, No.~254, 847--857 (2006; Zbl 1090.65151)], convergence orders 4r for the eigenvalue approximation and 3r for spectral subspace approximation are obtained for sufficiently smooth kernels, but the proposed methods are simpler and faster to implement. The authors consider also application of the methods to the case of discontinuous integral kernels along the diagonal and prove superconvergence results. Numerical examples confirm the theoretical results.
scientific article; zbMATH DE number 5914099
scientific article