71043 20180625152915.0 doi 10.1137/120864581 sideral 82204 ART-2013-82204 eng (orcid)0000-0002-8089-343X Barrio, Roberto Universidad de Zaragoza A General Condition Number for Polynomials 2013 Access copy available to the general public Unrestricted This paper presents a generic condition number for polynomials that is useful for polynomial evaluation of a finite series of polynomial basis defined by means of a linear recurrence. This expression extends the classical one for the power and Bernstein bases, but it also provides us a general framework for all the families of orthogonal polynomials like Chebyshev, Legendre, Gegenbauer, Jacobi, and Sobolev orthogonal polynomial bases. The standard algorithm for the evaluation of finite series in any of these polynomial bases is the extended Clenshaw algorithm. The use of this new condition number permits us to give a general theorem about the forward error for that evaluation algorithm. A running-error bound of the extended algorithm is also presented and all the bounds are compared in several numerical examples. info:eu-repo/grantAgreement/ES/MICINN/MTM2009-10767 info:eu-repo/grantAgreement/ES/MICINN/MTM2012-31883 info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 1.69 2013 MATHEMATICS, APPLIED 27 / 251 = 0.108 2013 Q1 T1 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Jiang, Hao (orcid)0000-0002-5701-1670 Serrano, Sergio Universidad de Zaragoza 2005 595 Universidad de Zaragoza Departamento de Matemática Aplicada Matemática Aplicada 51, 2 (2013), 1280-1294 SIAM j. numer. anal. SIAM JOURNAL ON NUMERICAL ANALYSIS 0036-1429 674002 http://zaguan.unizar.es/record/71043/files/texto_completo.pdf Versión publicada 80848 http://zaguan.unizar.es/record/71043/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:71043 articulos driver 2018-06-25-13:54:57 ARTICLE