Download Approximation Theory IX: Theoretical aspects by C. K. Chui, Larry L. Schumaker PDF

By C. K. Chui, Larry L. Schumaker

This meticulously edited collection of papers comes out of the 9th overseas Symposium on Approximation concept held in Nashville, Tennessee, in January, 1998. each one quantity comprises numerous invited survey papers written via specialists within the box, in addition to contributed examine papers.This booklet can be of significant curiosity to mathematicians, engineers, and computing device scientists operating in approximation conception, wavelets, computer-aided geometric layout (CAGD), and numerical analysis.Among the subjects integrated within the books are the following:adaptive approximationapproximation via harmonic functionsapproximation via radial foundation functionsapproximation by way of ridge functionsapproximation within the advanced planeBernstein polynomialsbivariate splinesconstructions of multiresolution analysesconvex approximationframes and body basesFourier equipment generalized moduli of smoothnessinterpolation and approximation through splines on triangulationsmultiwavelet basesneural networksnonlinear approximationquadrature and cubaturerational approximationrefinable functionssubdivision schemesthin plate splineswavelets and wavelet platforms

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Introduction The term pseudo-spectral method appears in numerical analysis of nonlinear evolution equations, and it is associated with hybrid strategies usually used for updating the approximate solution at each time step: the linear part is calculated in the Fourier space, and the nonlinear terms are evaluated in the physical domain. In wavelet analysis, similar pseudo-wavelet methods have been adopted [2, 3, 8, 10]. In these formulations, the evaluation of the nonlinear terms in physical space uses functionals defined in terms of point values.

Edu] VLADIMIR N. edu] D. edu] S. A. br] GENRIKH TS. de] JOSEPH D. O. jp] G. O. edu] Page xvii RAYMOND O. WELLS, JR. edu] HOLGER WENDLAND (**361), Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Lotzestr. , Kaiserstr. com] MARY F. de] PING ZHOU (*51), Department of Mathematics and Statistics, Simon Fraser University, Burnaby, B. ca] Page 1 On the Reproduction of Linear Functions by Local Trigonometric Bases Kai Bittner Abstract. Using an approach of Chui and Shi we construct smooth local trigonometric bases which reproduce linear functions locally by a finite set of basis functions.

Meyer, Remarques sur l'analyse de Fourier á fenêtre, C. R. Acad. Sci. Paris 312 (1991), 259-261. 6. , S. Jaffard, and J. L. Journé, A simple Wilson orthonormal basis with exponential decay, SIAM J. Math. Anal. 22 (1991), 554-572. 7. Jawerth, B. and W. Sweldens, Biorthogonal smooth local trigonometric bases, J. Fourier Anal. Appl. 2 (1995), 109-133. 8. , Optimized local trigonometric bases, Appl. Comput. Harmonic Anal. 3 (1996), 301-323. de Page 9 Discretization of Nonlinear Terms Using Biorthogonal Wavelets: Hybrid Formulations José E.

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