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Numerical approximation theory --- Wavelets (Mathematics) --- Ondelettes --- 517.518.8 --- 519.6 --- 681.3*G12 --- Wavelet analysis --- Harmonic analysis --- 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) --- Wavelets (Mathematics). --- 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 --- Analyse de fourier

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Harmonic analysis. Fourier analysis --- Wavelets (Mathematics) --- Electric filters --- Signal processing --- Mathematics --- #TELE:SISTA --- lineaire algebra --- geodesie --- gps (global positioning system) (global position system) --- 519.6 --- 681.3*G12 --- 681.3*I4 --- 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) --- Image processing: image displays image processing software (Computing methododologies) --- 681.3*I4 Image processing: image displays image processing software (Computing methododologies) --- 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 --- Algebras, Linear --- Geodesy --- Global Positioning System --- Algèbre linéaire --- GPS --- Traitement du signal --- Ondelettes --- Wavelets (Mathematics). --- 681.3*I4 Image processing: image displays; image processing software (Computing methododologies) --- Image processing: image displays; image processing software (Computing methododologies) --- 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) --- Mathematics. --- Mathématiques --- Fourier analysis --- Fourier, Analyse de. --- Ondelettes. --- MATLAB. --- MATLAB --- Numerical analysis --- Analyse numérique. --- Electric filters - Mathematics. --- Signal processing - Mathematics. --- Electric filters - Mathematics --- Signal processing - Mathematics

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519.65 <063> --- Computer graphics --- -Engineering design --- -Surfaces --- -#TELE:d.d. Prof. A. J. J. Oosterlinck --- 517.518.8 --- 681.3*G12 --- 681.3*I35 --- 681.3*I35 Computational geometry and object modeling (Computer graphics) --- Computational geometry and object modeling (Computer graphics) --- 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) --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Approximation of functions by polynomials and their generalizations --- Curved surfaces --- Geometry --- Shapes --- Design, Engineering --- Engineering --- Industrial design --- Strains and stresses --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- 519.65 <063> Approximation. Interpolation--Congressen --- Approximation. Interpolation--Congressen --- Congresses --- Data processing --- -Congresses --- Design --- Digital techniques --- Engineering design --- Surfaces --- #TELE:d.d. Prof. A. J. J. Oosterlinck --- 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) --- Data processing&delete& --- Infographie --- Conception technique --- Congrès --- Informatique --- BASIC (Computer program language)

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Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets and scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.

Approximation theory. --- Numerical analysis. --- Mathematical analysis --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Mathematics. --- Functions, special. --- Fourier analysis. --- Mathematical physics. --- Approximations and Expansions. --- Special Functions. --- Fourier Analysis. --- Mathematical Methods in Physics. --- Numerical Analysis. --- Physical mathematics --- Physics --- Analysis, Fourier --- Special functions --- Math --- Science --- Mathematics --- Approximation theory --- Fourier analysis --- Numerical analysis --- Spherical functions --- Spline theory --- Wavelets (Mathematics) --- 519.65 --- 681.3*G12 --- 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) --- 519.65 Approximation. Interpolation --- Approximation. Interpolation --- Wavelet analysis --- Harmonic analysis --- Spline functions --- Interpolation --- Functions, Spherical --- Spherical harmonics --- Transcendental functions --- Spheroidal functions --- Special functions. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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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