あるクラスの無限行列二重固有値計算法

概要

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It has been shown that a series of three-term recurrence relations of a certain class is a powerful tool for solving zeros of some special functions and eigenvalue problems (EVPs) of certain differential equations. Such cases include: the zeros of J_v(z); the zeros of zJ′_v(z)+HJ_v(z); the EVP of the Mathieu differential equation; and the EVP of the spheroidal wave equation. Previously by the author, it was demonstrated that the three-term recurrence relations of the class may be reformulated as two different EVPs for infinite complex symmetric tridiagonal matrices, and also was shown that a necessary and sufficient condition that such infinite matrices have double eigenvalues was given. In this article, as a succession of the previous research, algorithms for the computation of two types of double pairs are proposed in two ways: by Newton Raphson method of two variables, and by matrix method combined with, say, pseudo-Newton Raphson method. As an example, the problem of finding double eigenvalues of the Mathieu differential equation is solved with its experiments.
静岡産業大学の論文
2001-02-28