Verified computation of Lamé functions with high accuracy
type: Item
instance of: scholarly article
title: Verified computation of Lamé functions with high accuracy
zbMATH Open document ID: 0945.33001
DOI: 10.1007/BF02684331
author: H.-J. Dobner
author: Stefan Matthias Ritter
published in: Computing
publication date: 2000-10-03T00:00:00Z
review text: It is not common knowledge that a sufficiently accurate and efficient computation of higher transcendental functions creates serious problems, even nowadays. For instance, although Lamé (ellipsoidal) functions appear widely in mathematical physics involving ellipsoid geometry, a numerical method for their verified computation is a non trivial task. It is presented here. The necessary numerical tools applied here set high standards. They are e.~g. interval arithmetics (together with the use of algorithms due to \textit{S.~M.~Rump}, A new approach to scientific computation, Proc. Symp., Yorktown Heights, N. Y 1982, Notes Rep. Comput. Sci. Appl. Math. 7, 51-120 (1983; Zbl 0597.65018)), further precise computer arithmetics, so that no floating point number lies between the exact and rounded result of floating point numbers, and automatic differentiation. The high accuracy is illustrated by interval inclusions of various results for Lamé functions of first and second kind.
Mathematics Subject Classification ID: 33-04
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 33E10
zbMATH DE Number: 1112323
zbMATH Keywords: Lamé functions
zbMATH Keywords: interval arithmetics
reviewed by: E. Lanckau
MaRDI profile type: Publication
cites work: Q5732789
cites work: Q3846576
cites work: Q4481373
cites work: Q3139692
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cites work: Global convergence of tridiagonal QR algorithm with origin shifts
full work available at URL: https://doi.org/10.1007/bf02684331
OpenAlex ID: W2065973950
description: scientific article; zbMATH DE number 1112323