Computation of multiple eigenvalues of infinite tridiagonal matrices
Yoshinori Miyazaki, Nobuyoshi Asai, Yasushi Kikuchi, Dongsheng Cai, Yasuhiko Ikebe · Mathematics of Computation · 2003
In this paper, it is first given as a necessary and sufficient condition that infinite matrices of a certain type have double eigenvalues. The computation of such double eigenvalues is enabled by the Newton method of two variables. The three-term recurrence relations obtained from its eigenvalue problem (EVP) subsume the well-known relations of (A) the zeros of J ν ( z ) J_{ u }(z) ; (B) the zeros of z J ν ′ ( z ) + H J ν ( z ) zJ’_{ u }(z)+HJ_{ u }(z) ; (C) the EVP of the Mathieu differential equation; and (D) the EVP of the spheroidal wave equation. The results of experiments are shown for the three cases (A)–(C) for the computation of their “double pairs”.