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Padé approximant. --- Painlevé equations. --- Equations, Painlevé --- Functions, Painlevé --- Painlevé functions --- Painlevé transcendents --- Transcendents, Painlevé --- Differential equations, Nonlinear --- Approximant, Padé --- Approximation theory --- Continued fractions --- Polynomials --- Power series

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Numerical approximation theory --- Padé approximant --- Approximation theory --- Théorie de l'approximation --- Congresses --- Congrès --- Pade approximant --- 519.25 --- -Approximation theory --- -517.518.8 --- 519.6 --- 681.3*G12 --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Approximant, Padé --- Continued fractions --- Power series --- Statistical data handling --- Approximation of functions by polynomials and their generalizations --- Computational mathematics. Numerical analysis. Computer programming --- Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- Congresses. --- 681.3*G12 Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.518.8 Approximation of functions by polynomials and their generalizations --- 519.25 Statistical data handling --- Padé approximant --- Théorie de l'approximation --- Congrès --- 517.518.8 --- Approximation theory - Congresses --- Pade approximant - Congresses --- Approximation et developpements --- Approximation rationnelle --- Approximation de pade

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Numerical approximation theory --- Pade approximant --- 517.518.8 --- 519.6 --- 681.3*G12 --- Approximant, Padé --- Approximation theory --- Continued fractions --- Polynomials --- Power series --- Approximation of functions by polynomials and their generalizations --- Computational mathematics. Numerical analysis. Computer programming --- Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- Padé approximant. --- 681.3*G12 Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Padé approximant --- Approximation et developpements --- Approximation rationnelle --- Suites et series --- Approximation de pade --- Sommabilite

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Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Padé tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of fast algorithms for structured problems and shows how they deal with singular situations. Links are made with more applied subjects such as linear system theory and signal processing, and with more advanced topics and recent results such as general bi-orthogonal polynomials, minimal Padé approximation, poly

Ordered algebraic structures --- Numerical approximation theory --- Computer science --- lineaire algebra --- Algebras, Linear --- Euclidean algorithm --- Orthogonal polynomials --- Padé approximant --- #TELE:SISTA --- 519.6 --- 681.3*G11 --- 681.3*G12 --- 681.3*G13 --- Algorithm of Euclid --- Continued division --- Division, Continued --- Euclid algorithm --- Euclidian algorithm --- Euclid's algorithm --- Algorithms --- Number theory --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 681.3*G12 Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- 681.3*G11 Interpolation: difference formulas; extrapolation; smoothing; spline and piecewise polynomial interpolation (Numerical analysis) --- Interpolation: difference formulas; extrapolation; smoothing; spline and piecewise polynomial interpolation (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Fourier analysis --- Functions, Orthogonal --- Polynomials --- Approximant, Padé --- Approximation theory --- Continued fractions --- Power series --- Euclidean algorithm. --- Algebras, Linear. --- Padé approximant. --- Orthogonal polynomials. --- Padé approximant. --- Pade approximant.

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Differential equations --- Boundary value problems. --- Padé approximant. --- Riemann-Hilbert problems. --- Spectral theory (Mathematics) --- Spectral theory (Mathematics). --- Functions of complex variables --- Riemann-Hilbert problems --- Fonctions d'une variable complexe --- Riemann-Hilbert, Problèmes de --- Differential equations, Partial --- Équations aux dérivées partielles --- Eigenvalues --- Problèmes aux valeurs propres --- Boundary value problems --- Problèmes aux limites --- Équations aux dérivées partielles. --- Problèmes aux valeurs propres. --- Problèmes aux limites. --- Riemann-Hilbert, Problèmes de. --- Équations aux dérivées partielles. --- Problèmes aux valeurs propres. --- Problèmes aux limites. --- Riemann-Hilbert, Problèmes de.