Division algorithms for continued fractions and the Padé table

DOI10.1016/0771-050X(80)90034-0zbMath0445.65012MaRDI QIDQ1145465

Adhemar Bultheel

Publication date: 1980

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

zbMATH Keywords

continued fractionsdivision algorithmPade approximantsnon-normal Pade tablesawtooth algorithm

Mathematics Subject Classification ID

Padé approximation (41A21) Algorithms for approximation of functions (65D15) Continued fractions; complex-analytic aspects (30B70) Numerical summation of series (65B10) Convergence and divergence of continued fractions (40A15)

Related Items (8)

From matrix to vector Padé approximants ⋮ Formal orthogonal polynomials and Hankel/Toeplitz duality ⋮ Cayley's theorem and its application in the theory of vector Padé approximants ⋮ On the computation of non-normal Padé approximants ⋮ Perron fractions: An algorithm for computing the Padé table ⋮ On the use of a corresponding sequence algorithm for \(\delta\)-fractions ⋮ Recursive partial realization from the combined sequence of Markov parameters and moments ⋮ Nested-feedback-loops realization of 2-D systems

Cites Work

• Padé approximation and its applications. Proceedings of a conference held in Antwerp, Belgium, 1979
• A new look at the Padé table and the different methods for computing its elements
• Matrix interpretations and applications of the continued fraction algorithm
• Computation of Padé approximants and continued fractions
• A useful identity for the rational Hermite interpolation table
• A class of algorithms for obtaining rational approximants to functions which are defined by power series
• Approximants de Padé
• Solution of linear equations with Hankel and Toeplitz matrices
• Recursive Algorithms for Nonnormal Padé Tables
• A Property of Euclid’s Algorithm and an Application to Padé Approximation
• Numerical Aspects of Recursive Realization Algorithms
• Symbolic Computation of Padé Approximants
• The Solution of a Toeplitz Set of Linear Equations
• An Algorithm for the Inversion of Finite Toeplitz Matrices
• An Algorithm for the Inversion of Finite Hankel Matrices
• Toeplitz Matrix Inversion: The Algorithm of W. F. Trench
• The Triangular Decomposition of Hankel Matrices
• The Padé Table and Its Relation to Certain Algorithms of Numerical Analysis
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Division algorithms for continued fractions and the Padé table