A review of branched continued fraction theory for the construction of multivariate rational approximants

DOI10.1016/0168-9274(83)90006-5zbMath0644.65012OpenAlexW2045306405MaRDI QIDQ1102699

Annie A. M. Cuyt, Brigitte M. Verdonk

Publication date: 1988

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(83)90006-5

zbMATH Keywords

multivariate approximationbranched continued fraction

Mathematics Subject Classification ID

Approximation by rational functions (41A20) Multidimensional problems (41A63) Algorithms for approximation of functions (65D15) Continued fractions; complex-analytic aspects (30B70) Convergence and divergence of continued fractions (40A15)

Related Items (14)

Associated branched continued fractions with two independent variables ⋮ Multivariate reciprocal differences for branched Thiele continued fraction expansions ⋮ On the fast solution of Toeplitz-block linear systems arising in multivariate approximation theory ⋮ A Fitzpatrick algorithm for multivariate rational interpolation ⋮ A multidimensional generalization of the Rutishauser $qd$-algorithm ⋮ On the linearization methods for univariate Birkhoff rational interpolation ⋮ Vector valued rational interpolants over triangular grids. ⋮ The multidimensional generalization of \(g\)-fractions and their application. ⋮ A Neville-like method via continued fractions. ⋮ Multidimensional regular C-fraction with independent variables corresponding to formal multiple power series ⋮ The two-dimensional \(g\)-fraction with independent variables for double power series ⋮ On branched continued fractions rational interpolation over pyramid-typed grids ⋮ Block-based Thiele-like blending rational interpolation ⋮ How well can the concept of Padé approximant be generalized to the multivariate case?

Cites Work

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• Multivariate rational interpolation
• Thiele-type branched continued fractions for two-variable functions
• A review of multivariate Padé approximation theory
• Multivariate reciprocal differences for branched Thiele continued fraction expansions
• Branched continued fractions for double power series
• A two-variable generalization of the Stieltjes-type continued fraction
• Evaluation of Branched Continued Fractions using Block-Tridiagonal Linear Systems

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