A General Condition Number for Polynomials

Barrio, Roberto (Universidad de Zaragoza) ; Jiang, Hao ; Serrano, Sergio (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1137/120864581

Año: 2013

Publicado en: SIAM JOURNAL ON NUMERICAL ANALYSIS 51, 2 (2013), 1280-1294
ISSN: 0036-1429

Factor impacto JCR: 1.69 (2013)

Categ. JCR: MATHEMATICS, APPLIED rank: 27 / 251 = 0.108 (2013) - Q1 - T1

Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2009-10767
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2012-31883

Tipo y forma: Article (Published version)

Área (Departamento): Matemática Aplicada (Departamento de Matemática Aplicada)