Modern Developments in Multivariate Approximation

by Haussmann, Werner

• ISBN13: 9783764321956
• ISBN10: 3764321954
• Format: Hardcover
• Copyright: 2004-02-01
• Publisher: Birkhauser

Summary

This volume contains a selection of eighteen peer-reviewed articles that were presented at the 5th International Conference on Multivariate Approximation, held in Witten-Bommerholz in September 2002. The contributions cover recent developments of constructive approximation on manifolds, approximation by splines and kernels, subdivision techniques and wavelet methods. The main topics are: - applications of multivariate approximation in finance - approximation and stable reconstruction of images, data reduction - multivariate splines for Lagrange interpolation and quasi-interpolation - radial basis functions - spherical point sets - refinable function vectors and non-stationary subdivision - applications of adaptive wavelet methods - blending functions and cubature formulae - singularities of harmonic functions The book provides an overview of state-of-the-art developments in a highly relevant field of applied mathematics, with many links to computer science and geophysics.

Table of Contents

Participants	9	(8)
Scientific Program of the Conference	17	(4)
Multivariate Approximation Methods for the Pricing of Catastrophe-Linked Bonds
H. Albrecher, J. Hartfinger, and R.F. Tichy	21	(20)
Note on a Generalized Invariance Principle and its Relevance for Cap Discrepancy and Energy
J.S. Brauchart	41	(16)
On Properties of Nonstationary Divided Difference Vector Subdivision Schemes
M. Charma and C. Conti	57	(14)
Multivariate Balanced Vector-Valued Refinable Functions
C.K. Chuff and Q. Jiang	71	(32)
Transfinite Interpolation by Blending Functions, Best One-Sided L1-Approximation, and Cubature Formulae
D.P. Dryanov	103	(22)
Refining Oscillatory Signals by Non-Stationary Subdivision Schemes
N. Dyn, D. Levin, and A. Luzzatto	125	(18)
Asymptotic Error Expansions for Schoenberg Type Operators
K. Dziedziul and K. Jetter	143	(10)
On the Approximation Order and Numerical Stability of Local Lagrange Interpolation by Polyharmonic Splines
A. Iske	153	(14)
Isolated Singularities of Harmonic Functions
L. Karp and H.S. Shapiro	167	(8)
Two Applications of Adaptive Wavelet Methods
A. Kunoth	175	(28)
Almost Interpolation and Radial Basis Functions
A. Le Mehaute	203	(12)
Fundamental Splines on Triangulations
G. Nurnberger and F. Zeilfelder	215	(20)
Integer DCT-II by Lifting Steps
G. Plonka and M. Tasche	235	(18)
Approximation of Density Functions and Reconstruction of the Approximant
M. Reimer	253	(10)
On Some Multivariate Quadratic Spline Quasi-Interpolants on Bounded Domains
P. Sablonniere	263	(16)
How to Generate Smoother Refinable Functions from Given Ones
T. Sauer	279	(16)
Reconstructing Multivariate Functions from Large Data Sets
H. Wendland	295	(14)
Three Scale Versus Matrix Refinement Equations
G. Zimmermann	309