000129844 001__ 129844
000129844 005__ 20240112163659.0
000129844 0247_ $$2doi$$a10.1016/j.cpc.2018.05.004
000129844 0248_ $$2sideral$$a106057
000129844 037__ $$aART-2018-106057
000129844 041__ $$aeng
000129844 100__ $$0(orcid)0000-0002-8089-343X$$aBarrio, Roberto$$uUniversidad de Zaragoza
000129844 245__ $$aORTHOPOLY: A library for accurate evaluation of series of classical orthogonal polynomials and their derivatives
000129844 260__ $$c2018
000129844 5060_ $$aAccess copy available to the general public$$fUnrestricted
000129844 5203_ $$aWe 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).
000129844 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E48$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2015-64095-P
000129844 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000129844 590__ $$a3.309$$b2018
000129844 591__ $$aPHYSICS, MATHEMATICAL$$b2 / 55 = 0.036$$c2018$$dQ1$$eT1
000129844 591__ $$aCOMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS$$b29 / 106 = 0.274$$c2018$$dQ2$$eT1
000129844 592__ $$a1.262$$b2018
000129844 593__ $$aPhysics and Astronomy (miscellaneous)$$c2018$$dQ1
000129844 593__ $$aHardware and Architecture$$c2018$$dQ1
000129844 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000129844 700__ $$aDu, Peibing
000129844 700__ $$aJiang, Hao
000129844 700__ $$0(orcid)0000-0002-5701-1670$$aSerrano Pastor, Sergio$$uUniversidad de Zaragoza
000129844 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000129844 773__ $$g231 (2018), 146-162$$pComput. phys. commun.$$tCOMPUTER PHYSICS COMMUNICATIONS$$x0010-4655
000129844 8564_ $$s1344929$$uhttps://zaguan.unizar.es/record/129844/files/texto_completo.pdf$$yPostprint
000129844 8564_ $$s2054383$$uhttps://zaguan.unizar.es/record/129844/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000129844 909CO $$ooai:zaguan.unizar.es:129844$$particulos$$pdriver
000129844 951__ $$a2024-01-12-14:07:43
000129844 980__ $$aARTICLE