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Error analysis for the computation of zeros of regular Coulomb wave function and its first derivative |
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| Authors: | Yoshinori Miyazaki Yasushi Kikuchi DongSheng Cai Yasuhiko Ikebe |
| Institution: | Faculty of Communications and Informatics, Shizuoka Sangyo University, Surugadai 4-1-1, Fujieda, Shizuoka, 426-8668, Japan ; Department of Computer Software, The University of Aizu, Tsuruga, Ikkimachi, Aizuwakamatsu, Fukushima, 965-8580, Japan ; Institute of Information Sciences and Electronics, The University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki, 305-8573, Japan ; Department of Computer Software, The University of Aizu, Tsuruga, Ikkimachi, Aizuwakamatsu, Fukushima, 965-8580, Japan |
| 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. |
| Keywords: | Coulomb wave function eigenvalue problem for infinite matrices three-term recurrence relations error estimate |
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