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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Error analysis for the computation of zeros of regular Coulomb wave function and its first derivative


Authors: Yoshinori Miyazaki, Yasushi Kikuchi, DongSheng Cai and Yasuhiko Ikebe
Journal: Math. Comp. 70 (2001), 1195-1204
MSC (2000): Primary 34L16
Published electronically: March 24, 2000
MathSciNet review: 1710636
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Abstract:

In 1975 one of the coauthors, Ikebe, showed that the problem of computing the zeros of the regular Coulomb wave functions and their derivatives may be reformulated as the eigenvalue problem for infinite matrices. Approximation by truncation is justified but no error estimates are given there.

The class of eigenvalue problems studied there turns out to be subsumed in a more general problem studied by Ikebe et al. in 1993, where an extremely accurate asymptotic error estimate is shown.

In this paper, we apply this error formula to the former case to obtain error formulas in a closed, explicit form.


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Additional Information

Yoshinori Miyazaki
Affiliation: Faculty of Communications and Informatics, Shizuoka Sangyo University, Surugadai 4-1-1, Fujieda, Shizuoka, 426-8668, Japan
Email: yoshi@fujieda-ssu.ac.jp

Yasushi Kikuchi
Affiliation: Department of Computer Software, The University of Aizu, Tsuruga, Ikkimachi, Aizuwakamatsu, Fukushima, 965-8580, Japan
Email: kikuchi@u-aizu.ac.jp

DongSheng Cai
Affiliation: Institute of Information Sciences and Electronics, The University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki, 305-8573, Japan
Email: cai@is.tsukuba.ac.jp

Yasuhiko Ikebe
Affiliation: Department of Computer Software, The University of Aizu, Tsuruga, Ikkimachi, Aizuwakamatsu, Fukushima, 965-8580, Japan
Email: ikebe@u-aizu.ac.jp

DOI: http://dx.doi.org/10.1090/S0025-5718-00-01241-2
PII: S 0025-5718(00)01241-2
Keywords: Coulomb wave function, eigenvalue problem for infinite matrices, three-term recurrence relations, error estimate
Received by editor(s): July 27, 1999
Published electronically: March 24, 2000
Article copyright: © Copyright 2000 American Mathematical Society