129844 20240112163659.0 doi 10.1016/j.cpc.2018.05.004 sideral 106057 ART-2018-106057 eng Barrio, Roberto Universidad de Zaragoza (orcid)0000-0002-8089-343X ORTHOPOLY: A library for accurate evaluation of series of classical orthogonal polynomials and their derivatives 2018 We present the ORTHOPOLY software that permits to evaluate, efficiently and accurately, finite series of any classical family of orthogonal polynomials (Chebyshev, Legendre, ultraspherical or Gegenbauer, Jacobi, Hermite and Laguerre orthogonal polynomials) and their derivatives. The basic algorithm is the BCS-algorithm (Barrio-Clenshaw-Smith derivative algorithm), that permits to evaluate the th derivative of a finite series of orthogonal polynomials at any point without obtaining before the previous derivatives. Due to the presence of rounding errors, specially in the case of high order derivatives, we introduce the compensated BCS-algorithm, based on Error-Free Transformation techniques, that permits to relegate the influence of the conditioning of the problem up to second order in the round-off unit of the computer. The BCS and compensated BCS algorithms may also give running-error bounds to provide information about the accuracy of the evaluation process. The ORTHOPOLY software includes C and Matlab versions of all the algorithms, and they are designed to be easily used in longer softwares to solve physical, mathematical, chemical or engineering problems (illustrated on the Schrödinger equation for the radial hydrogen atom). Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/DGA/E48 info:eu-repo/grantAgreement/ES/MICINN/MTM2015-64095-P info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 3.309 2018 PHYSICS, MATHEMATICAL 2 / 55 = 0.036 2018 Q1 T1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS 29 / 106 = 0.274 2018 Q2 T1 1.262 2018 Physics and Astronomy (miscellaneous) 2018 Q1 Hardware and Architecture 2018 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Du, Peibing Jiang, Hao Serrano Pastor, Sergio Universidad de Zaragoza (orcid)0000-0002-5701-1670 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 231 (2018), 146-162 Comput. phys. commun. COMPUTER PHYSICS COMMUNICATIONS 0010-4655 1344929 http://zaguan.unizar.es/record/129844/files/texto_completo.pdf Postprint 2054383 http://zaguan.unizar.es/record/129844/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:129844 articulos driver 2024-01-12-14:07:43 ARTICLE