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), 719730
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 threeterm recurrence relations obtained from its eigenvalue problem (EVP) subsume the wellknown 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 4268668, Japan
Email:
yoshi@ssu.ac.jp
Nobuyoshi Asai
Affiliation:
School of Computer Science and Engineering, University of Aizu, Fukushimaken 9658580, Japan
Yasushi Kikuchi
Affiliation:
Faculty of Science, Division II, Tokyo University of Science, Tokyo, 1628601, Japan
DongSheng Cai
Affiliation:
Institute of Information Sciences and Electronics, University of Tsukuba, Ibaraki 3058573, Japan
Yasuhiko Ikebe
Affiliation:
Research Center for Information Science, Meisei University, Tokyo, 1918506, Japan
DOI:
http://dx.doi.org/10.1090/S0025571803015552
PII:
S 00255718(03)015552
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
