A new approach to the rational interpolation problem

DOI10.1016/0377-0427(90)90438-6zbMath0715.41018OpenAlexW2154358310MaRDI QIDQ752354

Adhemar Bultheel, Marc Van Barel

Publication date: 1990

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(90)90438-6

zbMATH Keywords

recursive algorithmNewton-Padé approachNewton-Padé rational interpolation problem

Mathematics Subject Classification ID

Approximation by rational functions (41A20) Interpolation in approximation theory (41A05)

Related Items (17)

The multipoint Padé table and general recurrences for rational interpolation ⋮ Discrete linearized least-squares rational approximation on the unit circle ⋮ On the linearization methods for univariate Birkhoff rational interpolation ⋮ Matrix Padé approximation: Definitions and properties ⋮ The Neville-like form of the Fitzpatrick algorithm for rational interpolation ⋮ On the use of Kronecker's algorithm in the generalized rational interpolation problem ⋮ On a linear interpolation problem for \(n\)-dimensional vector polynomials ⋮ The computation of non-perfect Padé-Hermite approximants ⋮ A generalized minimal partial realization problem ⋮ A reliable method for computing M-Padé approximants on arbitrary staircases ⋮ A reliable modification of the cross rule for rational Hermite interpolation ⋮ A general module theoretic framework for vector M-Padé and matrix rational interpolation ⋮ A new formal approach to the rational interpolation problem ⋮ A parallel algorithm for discrete least squares rational approximation ⋮ Stable row recurrences for the Padé table and generically superfast lookahead solvers for non-Hermitian Toeplitz systems ⋮ A fast Hankel solver based on an inversion formula for Loewner matrices ⋮ A new approach to the rational interpolation problem: The vector case

Cites Work

• Reliable rational interpolation
• On the structure of the Newton-Padé table
• A reliable and numerically stable program for rational interpolation of Lagrange data
• The Padé Table and Its Relation to Certain Algorithms of Numerical Analysis
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