Table Of ContentAigorithms for Approximation 11
Aigorithms for Approximation 11
Based on the proceedings of the Second International Conference on
Algorithms for Approximation, held at Royal Military College of SCience,
Shrivenham, July 1988
Edited by
J. C. Mason
Professor of Computational Mathematics,
Royal Military College of Science, Shrivenham, UK
and
M.G.Cox
Senior Principal Scientific Officer,
National Physical Laboratory, Teddington, UK
Springer-Science+Business Media, B.V.
First published in 1990 by Chapman and Hall Ltd
11 New Fetter Lane, London EC4P 4EE
©1990 Springer Science+Business Media Dordrecht
Originally published by Chapman and Hall in 1990.
Softcover reprint of the hardcover 1s t edition 1990
All rights reserved. No part of this book may be reprinted or
reprodueed. or utilized in any form or by any eleetronic, mechanieal
or other means, now known or hereajier invel1led, including
photoeopying and reeording, or in any information storage and
retrieval system, without permission in writing from the publisher.
British Library Cataloguing in Publication Data
International Conference on Algorithms far Approximation (2nd:
1988: Royal Military College of Science)
Algorithms for approximation 11.
1. Mathematics. Approximation. Algorithms
I. Title 11. Mason, J. C. III. Cox, M. G.
511'.4
Library of Congress Cataloging in Publication Data
International Conference on Algorithms far Approximation (2nd:
1988: Royal Military College of Science, Shrivenham, England)
Algarithms for approximation 11: based on the proceedings of
the Second International Confcrcncc on Algarithms for
Approximation, held at Royal Military College of Science,
Shrivcnham, July 1988/ edited by J. C. Mason and M. E. Cox.
p. cm.
Conference held July 12-15, 1988, and sponsored by the
Cranfield Institute of Technology.
Includes bibliographical references.
ISBN 978-0-412-34580-7 ISBN 978-1-4899-3442-0 (eBook)
DOI 10.1007/978-1-4899-3442-0
I. Approximation theory-Data processing-Congresses.
I. Mason, J. C. 11. Cox, M. E. (Malcolm E.)
III. Cranfield Institute of Technology. IV. Title.
V. Title: Algorithms for approximation, 2.
VI. Title: Algorithms for approximation. two.
QA221.I54 1988
511' .4-dc20
89-23868
CIP
We dedicate this book to the memory of Professor Jerry L. Fields of the
University of Alberta, who died recently. Jerry made significant contributions to
rational approximation and special functions, and was a very generous friend.
Contents
Contributors
Preface
Part One DEVELOPMENT OF ALGORITHMS
1. Spline Approximation 3
Constrained spline approximation of functions and 4
data based on constrained knot removal
E. Arge, M. Drehlen, T. Lyche* and K. Morken
Near real-time spline fitting of long sequences of 21
uniformly-spaced data
G. T. Anthonyt and M. G. Cox
An algorithm for knot location in bivariate least 30
squares spline approximation
M. Bozzinit and F. de Tisi
A knot placement strategy for least squares spline 37
fitting based on the use of local poly no mi al
approximations
M. G. Cox, P. M. Harrist and H. M. Jones
An algorithm for nonlinear splines with non 46
negativity constraints
G. Opfert
Spline curve fitting of digitized contours 54
C. Poriert and C. Vercken
A B-spline approximation algorithm for quasi 62
interpolation or filtering
C. Raburr
On knots and nodes for spline interpolation 72
P. W. Smitht
2. Polynomial and Piecewise Polynomial Approximation 79
A basis for certain spaces of multivariate polynomials ~o
and exponentials
W. Dahmen*
Monotone piecewise cubic data fitting 99
F. N. Fritscht
Direct and converse results on simultaneous 107
approximation by the method of Bernstein-
Durrmeyer operators
M. Heilmann and M. W. Mülled
Orthogonality and approximation in a Sobolev space 117
A. Iserlest, P. E. Koch, S. P. NrjJrsett and
1. M. Sanz-Serna
Piecewise polynomial approximation of polynomial 5
curves
M. A. Lachancet
Calculation of the energy of a piecewise polynomial 4
surface
E. Quakt and L. L. Schumaker
3. Interpolation 145
Radial basis function interpolation on an infinite 146
regular grid
M. D. Buhmannt and M. 1. D. Powell*
The Fourier operator of even order and its 170
application to an extremum problem in interpolation
L. Brutmant
On multivariate polynomial interpolation 177
N. Dynt and A. Ron
Algorithms for the construction of data dependent 1~5
triangulations
N. Dyn, D. Levin and S. Rippat
Algorithms for computing best parametric cubic 193
interpolation
C. Rademacher and K. Schered
4. Smoothing and Constraint Methods 209
Data fitting by penalized least squares 210
M. Von Golitschek and L. L. Schumaker*
A semiinfinite programming algorithm for 228
eonstrained best approximation
K. W. Boswortht
Inferenee region for a method of loeal approximation 236
by using the residuals
M. Bozzini and L. Lenarduzzit
5. Complex Approximation 245
Numerieal methods for Chebyshev approximation of 246
eomplex-valued funetions
G. A. Watson*
A fast algorithm for linear eomplex Chebyshev 265
approximation
P. T. P. Tangt
Part Two APPLICA TIONS 275
6. Computer Aided Design and Geometrie Modelling 277
Uniform subdivision algorithms for eurves and 278
surfaees
N. Dyn, J. A. Gregory* and D. Levin
Approximation by spheres 296
T. B. Boffeyt, M. G. Cox, L. M. Delves and C. J.
Pursglove
Interpolation of seattered data on a spherieal domain 303
T. A. Foleyt
Least squares best fit geometrie elements 311
A. B. Forbest
Uniform pieeewise approximation on the sphere 320
W. Freedent and 1. C.Mason
7. Applications in Numerieal Analysis 335
Approximation theory and numerieal linear algebra 336
L. N. Trefethen *
An algorithm for eomputing minimum norm solutions 361
of the finite moment problem
M. Frontinit, G. Rodriguez and S. Seatzu
Numerieal solution of the biharmonie equation using 369
different types of bivariate spline funetions
R. H. 1. Gmelig Meylingt
Quadrature solution of integral equations: a uniform 377
treatment of Fredholm and Volterra equations
G. O. Olaofet
Increasing the convergence modulus of an asymptotic 387
expansion: an algorithm for numerical differentiation
G. Walzt
Approximation and parameter estimation in ordinary 395
differential equations
J. Williamst
8. Applications in Other Disciplines 405
Applications of discrete LI methods in science and 406
engineering
C. Zala and 1. Barrodale*
Constrained complex approximation algorithms in 424
communication engineering
J. C. M ason *, A. E. Trefethen and S. 1. Wilde
Integration of absolute amplitude from a decibel 449
B-spline fit
R. W. Allent and J. G. Metcalfe
A nonlinear least squares data fitting problem arising 458
in microwave measurement
M. G. Cox and H. M. Jonest
A complex minimax algorithm for phase-only 466
adaptation in antenna arrays
J. C. Mason and S. J. Wildet
Part Three CATALOGUE OF ALGORITHMS 477
A catalogue of algorithms for approximation 479
E. Grosse*
* Invited Speaker
tSpeaker
Contributors
R. W. Allen
Allen Clarke Research Centre, Plessey Research Ltd, Caswell, Towcester,
Northamptonshire, UK.
G. T. Anthony
Division of Information Technology and Computing, National Physical
Laboratory, Teddington, Middlesex, UK.
E. Arge
Institut fur Informatikk, University of Oslo, Blindem, Oslo, Norway.
I. Barrodale
Barrodale Computing Services Ltd, Victoria, British Columbia, Canada.
T. B. Boffey
Department of Statistics and Computational Mathematics, University of
Liverpool, Liverpool, UK.
K. W. Bosworth
Department of Mathematics and Statistics, Utah State University, Logan,
Utah, USA.
M. Bozzini
Dipartimento di Matematica, Universita di Lecce, Lecce, Italy.
L. Brutman
Department of Mathematics and Computer Science, University of Haifa,
Haifa, Israel.
M. D. Buhmann
Department of Applied Mathematics and Theoretical Physics, University
of Cambridge, Cambridge, UK.
M. G. Cox
Division of Information Technology and Computing, National Physical
Laboratory, Teddington, Middlesex, UK.
M. DrehIen
Institut fur Informatikk, University of Oslo, Blindem, Oslo, Norway.
W. Dahmen
Fachbereich Mathematik (WE3), Freie Universität BerIin, BerIin, FRG.
L. M. Delves
Department of Statistics and Computational Mathematics, University of
Liverpool, Liverpool, UK.
