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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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Numerical approximation theory --- Approximation theory --- Spline theory --- Numerical analysis --- Congresses --- -Numerical analysis --- -Spline theory --- -519.6 --- 681.3*G11 --- 681.3*G12 --- 681.3*G14 --- Spline functions --- Interpolation --- Mathematical analysis --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Computational mathematics. Numerical analysis. Computer programming --- Interpolation: difference formulas; extrapolation; smoothing; spline and piecewise polynomial interpolation (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) --- Quadrature and numerical differentiation: adaptive quadrature; equal intervalintegration; error analysis; finite difference methods; gaussian quadrature; iterated methods; multiple quadrature --- 681.3*G14 Quadrature and numerical differentiation: adaptive quadrature; equal intervalintegration; error analysis; finite difference methods; gaussian quadrature; iterated methods; multiple quadrature --- 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) --- 681.3*G11 Interpolation: difference formulas; extrapolation; smoothing; spline and piecewise polynomial interpolation (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 519.6 --- Approximation theory - Congresses --- Spline theory - Congresses --- Numerical analysis - Congresses
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Interpolation spaces. --- Matrices. --- 512.64 --- 519.6 --- 681.3*G11 --- 681.3*G12 --- 681.3*G13 --- Linear and multilinear algebra. Matrix theory --- Computational mathematics. Numerical analysis. Computer programming --- Interpolation: difference formulas; extrapolation; smoothing; spline and piecewise polynomial interpolation (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) --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 681.3*G13 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) --- 681.3*G11 Interpolation: difference formulas; extrapolation; smoothing; spline and piecewise polynomial interpolation (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 512.64 Linear and multilinear algebra. Matrix theory --- Interpolation spaces --- Matrices --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Spaces, Interpolation --- Function spaces
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519.6 --- 681.3 *G18 --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations: difference methods elliptic equations finite element methods hyperbolic equations method of lines parabolic equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods elliptic equations finite element methods hyperbolic equations method of lines parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- #KVIV:BB --- Éléments finis, Méthode des --- Finite element method --- Analyse numérique. --- Numerical analysis --- Mathématiques --- Numerical analysis. --- Finite element method. --- Analyse numérique --- Éléments finis, Méthode des. --- Approximation de padé --- Interpolation polynomiale --- 681.3 *G10 --- Mathematical analysis --- Computerwetenschap--?*G10 --- 681.3*G12 --- 681.3*G15 --- 681.3*G15 Roots of nonlinear equations: convergence; error analysis; iterative methods;polynomials (Numerical analysis) --- Roots of nonlinear equations: convergence; error analysis; iterative methods;polynomials (Numerical analysis) --- 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 --- 681.3*G19 --- 681.3*G19 Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) --- Integral equations: Fredholm equations; integro-differential equations; Volterra equations (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) --- 681.3*G13 --- 681.3*G17 --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 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 --- Electromagnetism. Ferromagnetism --- Electrical engineering --- Analyse numérique
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