Mathematics of Computation

Author(s): Yoshinori Miyazaki; Nobuyoshi Asai; Yasushi Kikuchi; DongSheng Cai; Yasuhiko Ikebe.
Journal: Math. Comp. 73 (2004), 719-730.
MSC (2000): Primary 34L16
Posted: June 19, 2003
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Abstract: 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 $J_{\nu}(z)$ ; (B) the zeros of $zJ'_{\nu}(z)+HJ_{\nu}(z)$ ; (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''.

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Yoshinori Miyazaki
Affiliation: Faculty of Communications and Informatics, Shizuoka Sangyo University, Shizuoka 426-8668, Japan
Email: yoshi@ssu.ac.jp

Nobuyoshi Asai
Affiliation: School of Computer Science and Engineering, University of Aizu, Fukushima-ken 965-8580, Japan

Yasushi Kikuchi
Affiliation: Faculty of Science, Division II, Tokyo University of Science, Tokyo, 162-8601, Japan

DongSheng Cai
Affiliation: Institute of Information Sciences and Electronics, University of Tsukuba, Ibaraki 305-8573, Japan

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