Approximation Theory IX: Theoretical aspects

798 Pages·1998·14.81 MB·English

by  C. K. Chui

Approximation Theory IX. Vol. 2,
title: Computational Aspects Innovations in
Applied Mathematics
author: Chui, C. K.
publisher: Vanderbilt University Press
isbn10 | asin:
print isbn13: 9780826513267
ebook isbn13: 9780585159522
language: English
subject Approximation theory--Congresses.
publication date: 1998
lcc: QA221.A66 1998eb
ddc: 511/.4
subject: Approximation theory--Congresses.
Page i
Approximation Theory IX
Page ii
Innovations in Applied Mathematics
An international series devoted to the latest research in modem areas
of mathematics, with significant applications in engineering,
medicine, and the sciences.
Series Editor:
Larry L. Schumaker
Stevenson Professor of Mathematics
Vanderbilt University
Previously published titles include
Mathematical Methods for
Curves and Surfaces (1995)
Curves and Surfaces with
Applications in CAGD (1997)
Surface Fitting and
Multiresolution Methods (1997)
Mathematical Methods for
Curves and Surfaces II (1998)
Mathematical Models in
Medical and Health Science (1998)
Page iii
Approximation Theory IX
Volume 2. Computational Aspects
edited by
Charles K. Chui
Department of Mathematics
Texas A&M University
Larry L. Schumaker
Department of Mathematics
Vanderbilt University
V U P
ANDERBILT NIVERSITY RESS
Nashville & London
Page iv
Copyright © 1998 by Vanderbilt University Press
All Rights Reserved
No part of this publication may be reproduced or transmitted in any
form or by any means, electronic or mechanical, including photocopy,
recording, or any information storage and retrieval system, without
permission in writing from the publisher.
First Edition 1998
98 99 00 01 02 5 4 3 2 1
This publication is made from paper that meets the minimum
requirements of ANSI/NISO Z39.48 (R 1997) Permanence of Paper
for Printed Library Materials.
Manufactured in the United States of America
Page v
Contents
Preface viii
Contributors ix
On the Reproduction of Linear Functions by Local 1
Trigonometric Bases
Kai Bittner
Discretization of Nonlinear Terms Using Biorthogonal 9
Wavelets: Hybrid Formulations
José E. Castilho and Sônia M. Gomes
Interpolation by Cubic Splines on Triangulations 17
Oleg Davydov, Günther Nürnberger, and Frank Zeilfelder
Interpolation and Almost Interpolation by Weak 25
Chebyshev Spaces
Oleg Davydov and Manfred Sommer
A Hermite Subdivision Scheme for the Evaluation of the 33
Powell-Sabin 12-Split Element
Nira Dyn and Tom Lyche
Fast Fourier Transforms for Nonequispaced Data 39
Benedikte Elbel and Gabriele Steidl
Scattered Data Interpolation by C2 Quintic Splines Using 47
Energy Minimization
Kathleen W. Farmer and Ming-Jun Lai
On Smoothing for Multilevel Approximation with Radial 55
Basis Functions
Gregory E. Fasshauer
A Semi-Prewavelet Approach to Piecewise Linear 63
Prewavelets on Triangulations
Michael S. Floater and Ewald G. Quak
Refinable Spline Functions 71
Tim N. T. Goodman
How is a Vector Pyramid Scheme Affected by 97
Perturbation in the Mask?
Bin Han and Thomas A. Hogan
Approximation to Small Deformation of Surfaces and Its 105
Application
Matthew He and Chandra Kambhamettu
Biorthogonal Spline Approximation and Its Wavelet 113
Analysis
Tian Xiao He
Page vi
A New Sufficient Condition for the Orthonormality of 121
Refinable Functions
Wenjie He and Ming-Jun Lai
Optimal Triangulations and Smoothness Conditions for 129
Bivariate Splines
Don Hong, Huan-Wen Liu, and Ram Mohapatra
Norming Sets and Scattered Data Approximation on 137
Spheres
Kurt Jetter, Joachim Stöckler, and Joseph D. Ward
Radial Quasi Interpolation on S2 145
A. K. Kushpel and J. Levesley
Bivariate Spline Method for Navier-Stokes Equations: 153
Domain Decomposition Technique
Ming-Jun Lai and Paul Wenston
Divergence-Free Multiwavelets 161
Joseph D. Lakey, Peter R. Massopust, and Maria C.
Pereyra
On Intra-and Inter-orthogonal Scaling and Wavelet 169
Vectors
Jian-ao Lian
General Moments Evaluation of Scaling Functions and 179
Wavelets
Jian-ao Lian and George A. Roberts
Properly Posed Set of Nodes for Bivariate Lagrange 189
Interpolation
Xue-Zhang Liang and Chun-Mei Lu
On the Closure of the Union of Nested Subspaces of 197
R. A. Lorentz and W. R. Madych
Calculating Joint Spectral Radius of Matrices and Hölder 205
Exponent of Wavelets
Mohsen Maesumi
On Interpolation by Hermite Tension Splines of Arbitrary 213
Order
Miljenko Marusic
*
Recent Developments in Approximation via Positive 221
Definite Functions
Francis J. Narcowich
Simulation-Based Modeling 243
Alexa Nawotki and Hans Hagen
A Multiscale Method for the Evaluation of Wiener 251
Integrals
Erich Novak, Klaus Ritter, and Achim Steinbauer
Spline Interpolation on Convex Quadrangulations 259
Günther Nürnberger and Frank Zeilfelder