Mathematics of Computation

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

Author(s): Yoshinori Miyazaki; Yasushi Kikuchi; DongSheng Cai; Yasuhiko Ikebe.
Journal: Math. Comp. 70 (2001), 1195-1204.
MSC (2000): Primary 34L16
Posted: March 24, 2000
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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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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: 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
Posted: March 24, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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