A Montessus de Ballore theorem for multivariate Padé approximants

DOI10.1016/0021-9045(85)90147-9zbMath0556.41012OpenAlexW1967040586MaRDI QIDQ760865

Annie A. M. Cuyt

Publication date: 1985

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(85)90147-9

zbMATH Keywords

convergence theoremmultivariate Padé approximantsMontessus de Balloremultivariate meromorphic functions

Mathematics Subject Classification ID

Padé approximation (41A21)

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The need for knowledge and reliability in numeric computation: Case study of multivariate Padé approximation ⋮ Uniform convergence of rows of the Padé table for functions with smooth Maclaurin series coefficients ⋮ Nested multivariate Padé approximants ⋮ Reliable root detection with the qd-algorithm: When Bernoulli, Hadamard and Rutishauser cooperate ⋮ An adaptive strategy for the bivariate solution of finite element problems using multivariate nested Padé approximants ⋮ Continuity of approximation by least-squares multivariate Padé approximants ⋮ On the convergence of certain sequences of rational approximants to meromorphic functions in several variables ⋮ Convergence of the nested multivariate Padé approximants ⋮ Generalized multivariate Padé approximants ⋮ On rational interpolation to meromophic functions in several variables ⋮ Multivariate Padé approximation. ⋮ How well can the concept of Padé approximant be generalized to the multivariate case?

Cites Work

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• Multivariate Padé-approximants
• Padé approximants for operators: theory and applications
• Rational approximants to holomorphic functions in \(n\)-dimensions
• Generalizations of the theorem of de Montessus to two-variable approximants
• General Order Padè-type Rational Approximants Defined from Double Power Series

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