Computation of multiple eigenvalues of infinite tridiagonal matrices

Authors:
Yoshinori Miyazaki, Nobuyoshi Asai, Yasushi Kikuchi, DongSheng Cai and Yasuhiko Ikebe

Journal:
Math. Comp. **73** (2004), 719-730

MSC (2000):
Primary 34L16

Published electronically:
June 19, 2003

MathSciNet review:
2031402

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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 ; (B) the zeros of ; (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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Additional Information

**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

**Yasuhiko Ikebe**

Affiliation:
Research Center for Information Science, Meisei University, Tokyo, 191-8506, Japan

DOI:
https://doi.org/10.1090/S0025-5718-03-01555-2

Received by editor(s):
March 2, 2002

Received by editor(s) in revised form:
August 12, 2002

Published electronically:
June 19, 2003

Article copyright:
© Copyright 2003
American Mathematical Society