Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation
The Rayleigh-Ritz method yields a decreasing sequence \(\mu_r\) that approximates the desired eigenvalue \(\lambda \) of Mathieu function or of spheroidal wave function. The method produces also a sequence of elementary functions \(g\) that approximates the desired eigenfunction \(f\) of the same functions. This paper provides answers to some questions about the rate of convergence \(\mu _r\to \lambda \) and \(g_r \to f\) as \(r\to \infty \), to the error bounds for the maximum norm \(\| g_r -f \| _\infty \) and to other convergence properties of the method. Errors are investigated by interesting numerical experimentations.
scientific article; zbMATH DE number 2101899