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C. K. Chui - Approximation Theory IX: Theoretical aspects

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Book:
Approximation Theory IX: Theoretical aspects
Author:
C K Chui / Larry L Schumaker
Publisher:
Vanderbilt University Press
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Year:
1998
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This meticulously edited selection of papers comes out of the Ninth International Symposium on Approximation Theory held in Nashville, Tennessee, in January, 1998. Each volume contains several invited survey papers written by experts in the field, along with contributed research papers.This book should be of great interest to mathematicians, engineers, and computer scientists working in approximation theory, wavelets, computer-aided geometric design (CAGD), and numerical analysis.Among the topics included in the books are the following:adaptive approximationapproximation by harmonic functionsapproximation by radial basis functionsapproximation by ridge functionsapproximation in the complex planeBernstein polynomialsbivariate splinesconstructions of multiresolution analysesconvex approximationframes and frame basesFourier methods generalized moduli of smoothnessinterpolation and approximation by splines on triangulationsmultiwavelet basesneural networksnonlinear approximationquadrature and cubaturerational approximationrefinable functionssubdivision schemesthin plate splineswavelets and wavelet systems

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title Approximation Theory IX Vol 2 Computational Aspects Innovations - photo 1

title	:	Approximation Theory IX. Vol. 2, 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

VANDERBILT UNIVERSITY PRESS
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

On the Reproduction of Linear Functions by Local Trigonometric Bases

Kai Bittner

Discretization of Nonlinear Terms Using Biorthogonal Wavelets: Hybrid Formulations

Jos E. Castilho and Snia M. Gomes

Interpolation by Cubic Splines on Triangulations

Oleg Davydov, Gnther Nrnberger, and Frank Zeilfelder

Interpolation and Almost Interpolation by Weak Chebyshev Spaces

Oleg Davydov and Manfred Sommer

A Hermite Subdivision Scheme for the Evaluation of the Powell-Sabin 12-Split Element

Nira Dyn and Tom Lyche

Fast Fourier Transforms for Nonequispaced Data

Benedikte Elbel and Gabriele Steidl

Scattered Data Interpolation by C2 Quintic Splines Using Energy Minimization

Kathleen W. Farmer and Ming-Jun Lai

On Smoothing for Multilevel Approximation with Radial Basis Functions

Gregory E. Fasshauer

A Semi-Prewavelet Approach to Piecewise Linear Prewavelets on Triangulations

Michael S. Floater and Ewald G. Quak

Refinable Spline Functions

Tim N. T. Goodman

How is a Vector Pyramid Scheme Affected by Perturbation in the Mask?

Bin Han and Thomas A. Hogan

Approximation to Small Deformation of Surfaces and Its Application

Matthew He and Chandra Kambhamettu

105

Biorthogonal Spline Approximation and Its Wavelet Analysis

Tian Xiao He

113

Page vi

A New Sufficient Condition for the Orthonormality of Refinable Functions

Wenjie He and Ming-Jun Lai

121

Optimal Triangulations and Smoothness Conditions for Bivariate Splines

Don Hong, Huan-Wen Liu, and Ram Mohapatra

129

Norming Sets and Scattered Data Approximation on Spheres

Kurt Jetter, Joachim Stckler, and Joseph D. Ward

137

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