Algorithms for Approximation II: Based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988 PDF
Preview Algorithms for Approximation II: Based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988
Aigorithms 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.
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