TY - BOOK ID - 927367 TI - Linear algebra, rational approximation, and orthogonal polynomials AU - Bultheel, Adhemar. AU - Barel, Marc van PY - 1997 VL - 6 SN - 0444828729 9780444828729 9780080535524 0080535526 1281047600 9786611047603 PB - Amsterdam ; New York : Elsevier, DB - UniCat KW - Ordered algebraic structures KW - Numerical approximation theory KW - Computer science KW - lineaire algebra KW - Algebras, Linear KW - Euclidean algorithm KW - Orthogonal polynomials KW - Padé approximant KW - #TELE:SISTA KW - 519.6 KW - 681.3*G11 KW - 681.3*G12 KW - 681.3*G13 KW - Algorithm of Euclid KW - Continued division KW - Division, Continued KW - Euclid algorithm KW - Euclidian algorithm KW - Euclid's algorithm KW - Algorithms KW - Number theory KW - Linear algebra KW - Algebra, Universal KW - Generalized spaces KW - Mathematical analysis KW - Calculus of operations KW - Line geometry KW - Topology KW - 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems KW - Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems KW - 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) KW - Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) KW - 681.3*G11 Interpolation: difference formulas; extrapolation; smoothing; spline and piecewise polynomial interpolation (Numerical analysis) KW - Interpolation: difference formulas; extrapolation; smoothing; spline and piecewise polynomial interpolation (Numerical analysis) KW - 519.6 Computational mathematics. Numerical analysis. Computer programming KW - Computational mathematics. Numerical analysis. Computer programming KW - Fourier analysis KW - Functions, Orthogonal KW - Polynomials KW - Approximant, Padé KW - Approximation theory KW - Continued fractions KW - Power series KW - Euclidean algorithm. KW - Algebras, Linear. KW - Padé approximant. KW - Orthogonal polynomials. KW - Padé approximant. KW - Pade approximant. UR - https://www.unicat.be/uniCat?func=search&query=sysid:927367 AB - 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 ER -