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An important problem that arises in many scientific and engineering applications is that of approximating limits of infinite sequences which in most instances converge very slowly. Thus, to approximate limits with reasonable accuracy, it is necessary to compute a large number of terms, and this is in general costly. These limits can be approximated economically and with high accuracy by applying suitable extrapolation (or convergence acceleration) methods to a small number of terms. This state-of-the art reference for mathematicians, scientists and engineers is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. The methods discussed are geared toward common problems in scientific and engineering disciplines. It differs from existing books by concentrateing on the most powerful nonlinear methods, presenting in-depth treatments of them, and showing which methods are most effective for different classes of practical nontrivial problems.

Causality. --- Causation. --- Extrapolation. --- Population Characteristics. --- Research Design. --- Extrapolation --- 519.6 --- 681.3*G11 --- 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 --- Approximation theory --- Numerical analysis

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While most textbooks on Numerical Analysis discuss linear techniques for the solution of various numerical problems, this book introduces and illustrates nonlinear methods. It presents several nonlinear techniques resulting mainly from the use of Padé approximants and rational interpolants.

Analyse numérique --- Numerical analysis --- Numerieke analyse --- 517.518.8 --- 519.6 --- 681.3*G11 --- 681.3*G12 --- Mathematical analysis --- Approximation of functions by polynomials and their generalizations --- 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) --- 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 --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Analyse numérique --- ELSEVIER-B EPUB-LIV-FT --- Mathematical analysis. --- Numerical analysis. --- 517.1 Mathematical analysis --- Analyse numérique. --- Series (mathematique) --- Equations non lineaires --- Sommation --- Approximation des solutions

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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