## Numerical computation of the eigenvalues for the spheroidal wave equation with accurate error estimation by matrix method

Yoshinori Miyazaki, Nobuyoshi Asai, Dongsheng Cai, and Yasuhiko Ikebe

### Abstract

A method to compute the eigenvalues of the spheroidal wave equations is proposed, as an application of a theorem on eigenvalues of certain classes of infinite matrices. The computation of its inverse problem (namely, solving another parameter $c^2$ for given eigenvalue $\lambda$) is likewise given. As a result, precise and explicit error estimates are obtained for the approximated eigenvalues.

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### Key words

spheroidal wave equation, eigenvalue, numerical computation, error estimate, infinite symmetric tridiagonal matrix

34L16

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