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Orthogonal Polynomials and their Applications

Volume 1329 of the series Lecture Notes in Mathematics pp 1-19


Error estimate in pade approximation

  • Claude BrezinskiAffiliated withLaboratoire d'Analyse Numérique et d'Optimisation U.F.R. I.E.E.A., Université des Sciences et Techniques de Lille Flandres-Artois

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The aim of this paper is to extend Kronrod's procedure for estimating the error in Gaussian quadrature formulas to Padé approximation. Some results on Stieltjes polynomials are also given. Examples show the effectiveness of the method. The procedure is then applied to the ɛ-algorithm, which is a convergence acceleration method related to Padé approximation. General principles for estimating the error in series approximations and sequence transformations are also brought to light.