Rational approximations corresponding to Newton series (Newton-Padé approximants)

DOI10.1016/0021-9045(76)90081-2zbMath0336.30015OpenAlexW2062340528MaRDI QIDQ1230134

William B. Jones, Michael A. Gallucci

Publication date: 1976

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

Full work available at URL: https://doi.org/10.1016/0021-9045(76)90081-2

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Numerical interpolation (65D05) Algorithms for approximation of functions (65D15) Continued fractions; complex-analytic aspects (30B70)

Related Items

The multipoint Padé table and general recurrences for rational interpolation, A Favard theorem for rational functions, Szegö functions and multipoint Padé approximation, Reliable rational interpolation, Generalized Cauchy formulas and numerical differentiation, Positivity of continued fractions associated with rational Stieltjes moment problems, On approximation of meromorphic functions having index-pair \((p,q)\), Divergence of vector-valued rational interpolations to meromorphic functions, Rates of convergence of multipoint rational approximants and quadrature formulas on the unit circle, The convergence and continuity of rational functions closely related to Padé approximants, The convergence and continuity of rational functions closely related to Padé approximants, Two-point Padé tables and 𝑇-fractions, The multipoint Padé approximation problem and its Hankel vector, Continued fractions associated with the Newton-Padé table, Newton-Padé approximations for multivariate functions, Hermite interpolation: The barycentric approach, Moment problems and orthogonal functions

Cites Work

• Padé approximate as limits of rational functions of best approximation, real domain
• An extension of Saff's theorem on the convergence of interpolating rational functions
• An extension of Montessus de Ballore's theorem on the convergence of interpolating rational functions
• On Convergence of Padé Approximants
• The Padé Table and Its Relation to Certain Algorithms of Numerical Analysis
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