Advances in Multivariate Approximation

by Editor: Werner Haußmann (University Duisburg-Essen, Germany); Editor: Kurt Jetter (University Duisburg-Essen, Germany); Editor: Manfred Reimer (Universitä; t Dortmund, Germany)

• ISBN13: 9783527402366
• ISBN10: 3527402365
• Edition: 1st
• Format: Hardcover
• Copyright: 1999-11-01
• Publisher: Wiley-VCH

Summary

This volume deals with main results of the 3rd International Conference on Multivariate Approximation, organized by the University of Dortmund. Special emphasis is put on the following topics: Interpolation and approximation on spheres and balls, approximation by solutions of differential equations, construction of node systems, scattered data techniques.

Table of Contents

Participants	9	(6)
Scientific Program of the Conference	15	(4)
Problems of Approximation Theory in Discrete Geometry	19	(14)
N. N. Andreev
V. A. Yudin
Dense Vector Spaces of Universal Harmonic Functions	33	(10)
D. H. Armitage
Best One-sided L1--Approximation by Harmonic and Subharmonic Functions	43	(14)
D. H. Armitage
S. J. Gardiner
Numerical Stability of Fast Fourier Transforms	57	(16)
G. Baszenski
R. Xuefang
M. Tasche
The Saturation Theorem for Box Spline Orthogonal Projection	73	(11)
M. Beska
K. Dziedziul
Problem on Monotonic Behaviour of Bernstein Operators	84	(1)
M. Beska
K. Dziedziul
Best One-Sided L1--Approximation by Blending Functions	85	(22)
B. D. Bojanov
D. P. Dryanov
W. Haußmann
G. P. Nikolov
On the Asymptotics of Points which Maximize Determinants of the Form det [g(|xi--xi|)]	107	(22)
L. Bos
U. Maier
Besov Regularity for the Stokes Problem	129	(10)
S. Dahlke
Optimal Periodic Interpolation in Multivariate Periodic Hilbert Spaces	139	(12)
F.-J. Delvos
Multiscale Modelling from Geopotential Data	151	(24)
W. Freeden
O. Glockner
R. Litzenberger
On a Family of Orthogonal Wavelets on the Quincunx Grid: Open Regularity Questions	175	(10)
A. Gottscheber
G. Steidl
Average Case Analysis of Numerical Integration	185	(16)
P. J. Grabner
P. Liardet
R. F. Tichy
Cubature Formulas on Spheres	201	(12)
H. Konig
Numerical Calculation of Spherical Designs	213	(14)
U. Maier
On Bivariate Spline Spaces	227	(4)
G. Nurnberger
F. Zeilfelder
Spherical Polynomial Approximations: A Survey	231	(22)
M. Reimer
Range Restricted Interpolation by Cubic C1--Splines on Clough--Tocher Splits	253	(16)
J. W. Schmidt
Some Error Estimates for Periodic Interpolation of Functions from Besov Spaces	269	(20)
W. Sickel
F. Sprengel
The Uniform Error of Hyperinterpolation on the Sphere	289	(18)
I. H. Sloan
R. S. Womersley
Simultaneous Approximation in the Dirichlet Space	307	(14)
A. Stray
The Equivalence between Weighted K--Functionals and Moduli of Smoothness on a Simplex and their Applications	321
P.-C. Xuan