{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T11:05:23Z","timestamp":1776769523899,"version":"3.51.2"},"reference-count":10,"publisher":"American Mathematical Society (AMS)","issue":"235","license":[{"start":{"date-parts":[[2001,3,24]],"date-time":"2001-03-24T00:00:00Z","timestamp":985392000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>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.<\/p>","DOI":"10.1090\/s0025-5718-00-01241-2","type":"journal-article","created":{"date-parts":[[2002,11,6]],"date-time":"2002-11-06T14:02:22Z","timestamp":1036591342000},"page":"1195-1204","source":"Crossref","is-referenced-by-count":10,"title":["Error analysis for the computation of zeros of regular Coulomb wave function and its first derivative"],"prefix":"10.1090","volume":"70","author":[{"given":"Yoshinori","family":"Miyazaki","sequence":"first","affiliation":[]},{"given":"Yasushi","family":"Kikuchi","sequence":"additional","affiliation":[]},{"given":"DongSheng","family":"Cai","sequence":"additional","affiliation":[]},{"given":"Yasuhiko","family":"Ikebe","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,3,24]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"783","DOI":"10.2307\/2371336","article-title":"Ring homomorphisms which are also lattice homomorphisms","volume":"61","author":"Ward, Morgan","year":"1939","journal-title":"Amer. 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Ikebe, Matrix Methods for the Numerical Solution of \ud835\udc67\ud835\udc3d\u2019_{\ud835\udf08}(\ud835\udc67)+\ud835\udc3b\ud835\udc3d_{\ud835\udf08}(\ud835\udc67)=0, Electronics and Communications in Japan, Part 3, Vol. 80, No. 7 (1997), 44-54.","DOI":"10.1002\/(SICI)1520-6440(199707)80:7<44::AID-ECJC6>3.0.CO;2-1"},{"key":"4","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1137\/1009002","article-title":"Computational aspects of three-term recurrence relations","volume":"9","author":"Gautschi, Walter","year":"1967","journal-title":"SIAM Rev.","ISSN":"https:\/\/id.crossref.org\/issn\/1095-7200","issn-type":"print"},{"key":"5","doi-asserted-by":"publisher","first-page":"878","DOI":"10.2307\/2005300","article-title":"The zeros of regular Coulomb wave functions and of their derivatives","volume":"29","author":"Ikebe, Yasuhiko","year":"1975","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"6","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/0024-3795(93)90112-2","article-title":"The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of \ud835\udc3d\u2080(\ud835\udc67)-\ud835\udc56\ud835\udc3d\u2081(\ud835\udc67) and of Bessel functions \ud835\udc3d\u2098(\ud835\udc67) of any real order \ud835\udc5a","volume":"194","author":"Ikebe, Yasuhiko","year":"1993","journal-title":"Linear Algebra Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-3795","issn-type":"print"},{"key":"7","unstructured":"Y. Miyazaki, N. Asai, D. Cai, and Y. Ikebe, A Numerical Computation of the Inverse Characteristic Values of Mathieu\u2019s Equation, Transactions of the Japan Society for Industrial and Applied Mathematics, 8(2), (1998), 199-222 (in Japanese)."},{"key":"8","unstructured":"Y. Miyazaki, N. Asai, D. Cai, and Y. Ikebe, The Computation of Eigenvalues of Spheroidal Differential Equations by Matrix Method, JSIAM Annual Meeting, (1997), 224-225 (in Japanese)."},{"key":"9","series-title":"Dover Books on Advanced Mathematics","isbn-type":"print","volume-title":"Functional analysis","author":"Riesz, Frigyes","year":"1990","ISBN":"https:\/\/id.crossref.org\/isbn\/0486662896"},{"key":"10","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1002\/sapm1939181153","article-title":"A function related to the series for \ud835\udc52^{\ud835\udc52^{\ud835\udc65}}","volume":"18","author":"Epstein, Leo F.","year":"1939","journal-title":"J. Math. Phys. Mass. Inst. 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