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This book on box splines is the first book giving a complete development for any kind of multivariate spline. Box splines give rise to an intriguing and beautiful mathematical theory that is much richer and more intricate than the univariate case because of the complexity of smoothly joining polynomial pieces on polyhedral cells. The purpose of this book is to provide the basic facts about box splines in a cohesive way with simple, complete proofs, many illustrations, and with an up-to-date bibliography. It is not the book's intention to be encyclopedic about the subject, but rather to provide the fundamental knowledge necessary to familiarize graduate students and researchers in analysis, numerical analysis, and engineering with a subject that surely will have as many widespread applications as its univariate predecessor. This book will be used as a supplementary text for graduate courses. The book begins with chapters on box splines defined, linear algebra of box spline spaces, and quasi-interpolants and approximation power. It continues with cardinal interpolation and difference equations, approximation by cardinal splines and wavelets. The book concludes with discrete box splines and linear diophantine equations, and subdivision algorithms.
Spline theory. --- Spline theory --- 517.518.8 --- 519.6 --- 681.3*G12 --- Spline functions --- Approximation theory --- Interpolation --- 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) --- 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
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Numerical approximation theory --- Courbes empiriques --- Curve fitting --- Fitting [Curve] --- Spline theory --- Splines [Theorie des ] --- Splines [Theorie van de ] --- 519.65 --- 517.518.8 --- 519.6 --- 681.3*G12 --- 681.3*J6 --- Spline functions --- Approximation theory --- Interpolation --- Fitting, Curve --- Numerical analysis --- Least squares --- Smoothing (Numerical analysis) --- Statistics --- Approximation. Interpolation --- 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) --- Computer-aided engineering: computer-aided design; CAD; computer-aided manufacturing; CAM --- Graphic methods --- 681.3*J6 Computer-aided engineering: computer-aided design; CAD; computer-aided manufacturing; CAM --- 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 --- 519.65 Approximation. Interpolation
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Computer science --- Numerical approximation theory --- Pitman's measure of closeness --- Wavelets --- Wavelets (Mathematics) --- 534 --- #TELE:MI2 --- 517.518.8 --- 519.6 --- 681.3*G12 --- Wavelet analysis --- Harmonic analysis --- Vibrations. Acoustics --- 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) --- Pitman's measure of closeness. --- 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 --- 534 Vibrations. Acoustics
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Geometry --- Mathematical models --- Computer graphics --- Data processing --- Congresses --- 517.518.8 --- 519.6 --- 681.3*G11 --- 681.3*G12 --- 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 --- Geometry - Data processing - Congresses --- Mathematical models - Congresses --- Computer graphics - Congresses
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