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Mathematics of Computation

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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 $ 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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Additional Information

Yoshinori Miyazaki
Affiliation: Faculty of Communications and Informatics, Shizuoka Sangyo University, Shizuoka 426-8668, Japan

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

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