Topics in Multivariate Approximation and InterpolationKurt Jetter, Martin Buhmann, Werner Haussmann, Robert Schaback, Joachim Stoeckler Elsevier, 2005 M11 15 - 356 pages This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for graduate students specializing in these topics, and for researchers in universities and in industry.
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Contents
| 1 | |
| 23 | |
| 39 | |
| 55 | |
Adaptive Wavelets for Sparse Representations of Scattered Data | 85 |
ReadytoBlossom Bases in Chebyshev Spaces | 109 |
Structural Analysis of Subdivision Surfaces A Summary | 149 |
Polynomial Interpolation in Several Variables Lattices Differences and Ideals | 191 |
Computational Aspects of Radial Basis Function Approximation | 231 |
Learning Theory From Regression to Classification | 257 |
Coherent States from Nonunitary Representations | 291 |
Index | 341 |
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Common terms and phrases
1)-dimensional Aided Geometric Design algorithm analysis applications Approximation Theory B-spline Banach space bases Bernstein blossoms bounded box spline characteristic map coefficients Computer Aided Geometric consider construction continuous contragredient representation control points control polygons convergence convex corresponding curvature curve data set decomposition defined Definition degree reducing interpolation denote derivatives diagonal domain EC-space eigenvalue element equations error exists finite formula function f given Hermite interpolation Hilbert space hyperplanes ideal inner product interpolation problem interpolation space L. L. Schumaker Lemma linear schemes linearly independent loss function Math matrix mesh methods minimal normal orthogonal outlier parameter parameterization piecewise polynomial interpolation positive prewavelets Proc proof quasi-interpolants radial basis functions refinement representation result satisfies scattered data Section sequence smoothness spline functions spline rings square integrable subdivision schemes subdivision surfaces subset subspace support vector machines Theorem triangulation unitary vanishes variables vector W-space wavelet zero
Popular passages
Page 192 - I am not writing about, because there's nothing so special about that; every story one chooses to tell is a kind of censorship, it prevents the telling of other tales ... I must get back to my fairy-story, because things have been happening while I've been talking too much.
Page 37 - Proceedings 3rd IEEE Conference on Control Applications, 3, pp. 1551-1556. [9] Powell, MJD, 1992, 'The Theory of Radial Basis Function Approximation in 1990,' in Advances in Numerical Analysis, Vol.
Page 2 - The structure of the paper is as follows. In section 2 we give some geometric preliminaries originally introduced in (Fam and Meditch, 1978) for stability problems.
Page 81 - A semi-prewavelet approach to piecewise linear prewavelets on triangulations, in: Approximation Theory IX, Vol. 2: Computational Aspects (CK Chui and LL Schumaker, Eds.), Vanderbilt University Press, Nashville, 1998, pp.
Page 128 - We would like to draw the reader's attention to the fact that our proofrule deals with what might be called "top-level fairness.
Page 147 - Goodman, TNT, Total positivity and the shape of curves, in Total Positivity and its Applications (M. Gasca and CA Micchelli eds.). Kluwer Academic Publishers, 1990.
Page 185 - Cirak, F., Ortiz, M. and Schroder, P., Subdivision surfaces: A new paradigm for thin-shell finite element analysis, Int. J. Numer.
Page 288 - Support vector machines and the Bayes rule in classification. Data Mining and Knowledge Discovery 6, 259-275.
Page 107 - Lee, S., Wolberg, G. and Shin, SY, Scattered data Interpolation with multilevel B-splines, IEEE Transactions on Visualization and Computer Graphics, Vol.