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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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Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.

Numerical analysis. --- Matrices --- Semiseparable matrices. --- Mathematical analysis --- Semi-separable matrices --- Data processing.

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