On the convergence of Padé-type approximants to analytic functions

DOI10.1016/0377-0427(84)90059-1zbMath0538.65011OpenAlexW1973388274MaRDI QIDQ793490

Michael Eiermann

Publication date: 1984

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(84)90059-1

zbMATH Keywords

rational functionsPadé-type approximationsequence transformationnumerical analytic continuationOkada theoremStieltjes and Hamburger moment problems

Mathematics Subject Classification ID

Matrix methods for summability (40C05) Approximation in the complex plane (30E10) Padé approximation (41A21) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Analytic continuation of functions of one complex variable (30B40) Function-theoretic methods (including power series methods and semicontinuous methods) for summability (40C15)

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Transmittance of a circular aperture by an integrable fractional-like approximation to \(J_ 0(x)\) function ⋮ Padé-type approximants of entire functions and acceleration of convergence: Two examples ⋮ Padé-type rational and barycentric interpolation ⋮ From numerical quadrature to Padé approximation ⋮ Resummation of formal series. Solutions of second order linear complex ordinary differential equations near irregular singularities ⋮ Quantifying the ill-conditioning of analytic continuation ⋮ Padé-type approximants and a summability theorem by Eiermann ⋮ Best choice of the pole for the Padé-type approximant of a Stieljes function ⋮ Composed Padé-type approximation ⋮ The convergence of Padé-type approximants to holomorphic functions of several complex variables ⋮ A complex coefficient rational approximation of \(\sqrt{1+x}\) ⋮ Orthonormality in Interpolation Schemes for Reconstructing Signals ⋮ Convergence Acceleration of Alternating Series

Cites Work

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