The Rayleigh-Ritz method still competitive

AbstractAn extended Rayleigh-Ritz method for computing two-sided eigenvalue bounds of the one-dimensional Schrödinger equation is presented. The method is based on the B-spline approximation over the truncated domain. For the low-lying eigenvalues and problems with rapidly increasing spectrum the corresponding lower bounds are much more accurate than the known Temple bounds. Numerical results for problems exhibiting different kinds of the eigenfunction behaviour are presented