000071043 001__ 71043
000071043 005__ 20180625152915.0
000071043 0247_ $$2doi$$a10.1137/120864581
000071043 0248_ $$2sideral$$a82204
000071043 037__ $$aART-2013-82204
000071043 041__ $$aeng
000071043 100__ $$0(orcid)0000-0002-8089-343X$$aBarrio, Roberto$$uUniversidad de Zaragoza
000071043 245__ $$aA General Condition Number for Polynomials
000071043 260__ $$c2013
000071043 5060_ $$aAccess copy available to the general public$$fUnrestricted
000071043 5203_ $$aThis 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.
000071043 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2009-10767$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2012-31883
000071043 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000071043 590__ $$a1.69$$b2013
000071043 591__ $$aMATHEMATICS, APPLIED$$b27 / 251 = 0.108$$c2013$$dQ1$$eT1
000071043 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000071043 700__ $$aJiang, Hao
000071043 700__ $$0(orcid)0000-0002-5701-1670$$aSerrano, Sergio$$uUniversidad de Zaragoza
000071043 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDepartamento de Matemática Aplicada$$cMatemática Aplicada
000071043 773__ $$g51, 2 (2013), 1280-1294$$pSIAM j. numer. anal.$$tSIAM JOURNAL ON NUMERICAL ANALYSIS$$x0036-1429
000071043 8564_ $$s674002$$uhttp://zaguan.unizar.es/record/71043/files/texto_completo.pdf$$yVersión publicada
000071043 8564_ $$s80848$$uhttp://zaguan.unizar.es/record/71043/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000071043 909CO $$ooai:zaguan.unizar.es:71043$$particulos$$pdriver
000071043 951__ $$a2018-06-25-13:54:57
000071043 980__ $$aARTICLE