Trends and Applications in Constructive Approximation

300 Pages·2005·4.44 MB·English

by  José Antonio Adell (auth.)

ISNM
International Series of Numerical Mathematics
Volume 151
Managing Editors:
K.-H. Hoffmann, Bonn
D. Mittelmann, Tempe
Associate Editors:
R. E. Bank, La Jolla
H. Kawarada, Chiba
R. J. LeVeque, Seattle
C. Verdi, Milano
Honorary Editor:
J. Todd, Pasadena
Trends and Applications in
Constructive Approximation
Detlef H. Mache
József Szabados
Marcel G. de Bruin
Editors
Birkhäuser Verlag
Basel . Boston . Berlin
Editors:
Detlef H. Mache Marcel G. de Bruin
University of Applied Science Bochum Department of Applied Mathematics
FB3, Applied Mathematics Delft University of Technology
(Constructive Approximation) P.O. Box 5031
Herner Str. 45 2600 GA Delft
D-44787 Bochum The Netherlands
József Szabados
Alfréd Rényi Institute of Mathematics
Hungarian Academy of Sciences
P.O. Box 127
H-1364 Budapest
2000 Mathematics Subject Classification 41Axx, 65Dxx
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA
Bibliographic information published by Die Deutsche Bibliothek
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in the Internet at http://dnb.ddb.de.
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ISBN 3-7643-7124-2 Birkhäuser Verlag, Basel – Boston – Berlin
© 2005 Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland
Part of Springer Science+Business Media
Printed on acid-free paper produced of chlorine-free pulp. TCF ∞
Printed in Germany
ISBN-10: 3-7643-7124-2
ISBN-13: 978-3-7643-7124-1
9 8 7 6 5 4 3 2 1 www.birkhauser.ch
Table of Contents
Preface .................................................................. vii
List of Participants ...................................................... ix
Scientific Program ....................................................... xiii
Jos´e Antonio Adell and Alberto Lekuona
Best Poisson Approximation of Poisson Mixtures.
A Linear Operator Approach ....................................... 1
Francesco Altomare and Ioan Rasa
On Some Classes of Diffusion Equations and
Related Approximation Problems ................................... 13
Jean-Paul Berrut, Richard Baltensperger and Hans D. Mittelmann
Recent Developments in Barycentric Rational Interpolation ......... 27
Dietrich Braess
Approximation on Simplices and OrthogonalPolynomials ........... 53
Marcel G. de Bruin and Detlef H. Mache
(0,2) Pa´l-type Interpolation: A General Method for Regularity ...... 61
Emil Ca˘tina¸s
Sufficient Convergence Conditions for Certain
Accelerated Successive Approximations ............................. 71
Teodora Ca˘tina¸s
The Combined Shepard-Lidstone Bivariate Operator ................ 77
Oleg Davydov, Alessandra Sestini and Rossana Morandi
Local RBF Approximation for Scattered Data
Fitting with Bivariate Splines ....................................... 91
Christian Igel, Stefan Wiegand and Frauke Friedrichs
Evolutionary Optimization of Neural Systems:
The Use of Strategy Adaptation .................................... 103
vi IBoMAT 2004 – Table of Contents
Detlef H. Mache and Jennifer Meyer
Finding Relevant Input Arguments
with Radial Basis Function Networks ............................... 125
Marie-Laurence Mazure
Subdivision Schemes and Non Nested Grids ......................... 135
Hrushikesh N. Mhaskar
A Markov-BernsteinInequality for Gaussian Networks .............. 165
Kai Michels
TS Control – The Link between Fuzzy Control
and Classical Control Theory ....................................... 181
Josef Obermaier and Ryszard Szwarc
Polynomial Bases for Continuous Function Spaces ................... 195
Frank Platte, Dmitri Kuzmin, Christoph Fredebeul and Stefan Turek
Novel Simulation Approaches for Cyclic Steady-state
Fixed-bed Processes Exhibiting Sharp Fronts and Shocks ............ 207
Ioan Rasa
Semigroups Associated to Mache Operators (II) ..................... 225
Paul Sablonni`ere
Recent Progresson Univariate and Multivariate Polynomial
and Spline Quasi-interpolants ....................................... 229
J´ozsef Szabados
A Strong Converse Result for Approximation by Weighted
Bernstein Polynomials on the Real Line ............................. 247
Christian Igel, Marc Toussaint and Wan Weishui
Rprop Using the Natural Gradient .................................. 259
Biancamaria Della Vecchia, Giuseppe Mastroianni and Peter V´ertesi
Some Properties of Quasi-orthogonaland
Para-orthogonalPolynomials.A Survey ............................. 273
Preface
During the last years, constructive approximation has reached out to encom-
pass the computational and approximation-theoretical aspects of different fields
in applied mathematics, including multivariate approximation methods, quasi-
interpolation, and multivariate approximation by (orthogonal) polynomials, as
well as modern mathematical developments in neuro fuzzy approximation, RBF-
networks, industrial and engineering applications.
FollowingthetraditionofourinternationalBommerholzconferencesin1995,
1998, and 2001 we regard this 4th IBoMAT meeting as an important possibility
forspecialistsinthefieldofappliedmathematicstocommunicateaboutnewideas
withcolleaguesfrom15differentcountriesalloverEuropeandasfarawayasNew
Zealand and the U.S.A. The conference in Witten Bommerholz was, as always,
held in a very friendly and congenial atmosphere.
The IBoMAT-serieseditorDetlef H. Mache(Bochum)wouldlike to congrat-
ulate Marcel de Bruin (Delft) and Jo´zsef Szabados (Budapest) for an excellent
editing job of this 4th volume about Trends and Applications in constructive ap-
proximation.
After the previous three published books in Akademie Verlag (1995) and
Birkha¨user Verlag (1999 and 2003) we were pleased with the high quality of the
contributions which could be solicited for the book. They are refereed and we
should mention our gratitude to the referees and their reports.
At this point we also thank the Deutsche Forschungsgemeinschaft (DFG,
Bonn) for providing the majority of the financial support of this 4th conference
and the publisher Birkha¨user / Springer Publishing Group for accepting the pro-
ceedings into its International Series of Numerical Mathematics.
AlsowewouldliketothankallparticipantsfortheireffortsinmakingIBoMat
2004 a more than successful conference.
Finally, we would like to express our special thanks to Petra Mache who
assisted in the preparation of this book and Jennifer Meyer who produced the
manuscript in a camera-ready form. We wish to express our appreciation of their
friendly assistance and wonderful cooperation.
The very positive resonance of the IBoMAT conferences in the years 1995,
1998,2001and2004willencourageusto continuethis successfulseriesinWitten-
Bommerholz with new international developments in applied mathematics and
applications in constructive approximation.
Witten-Bommerholz, January 2005 Marcel de Bruin (Delft)
Detlef H. Mache (Bochum)
Jo´zsef Szabados (Budapest)
Participants of the IBoMAT Conference in Witten-Bommerholz
D.H.Mache and E. Becker
List of Participants
• Adell, Jose A., Universidad de Zaragoza,Dept. de Metodos Estadisticos,
Facultad de Ciencias, E-50009 Zaragoza,Spain;
e-mail: [email protected]
• Altomare, Francesco, University of Bari, Department of Mathematics,
Campus Universitario, Via E. Orabona 4, 70125 Bari, Italy;
e-mail: [email protected]
• Beatson, Rick, University of Canterbury, Department of Mathematics and
Statistics, Private Bag 4800, Christchurch, New Zealand;
e-mail: [email protected]
• Berrut, Jean-Paul, Universit´e de Fribourg, D´epartment of Math´ematiques,
CH-1700 Fribourg / P´erolles,Switzerland;
e-mail: [email protected]
• Braess, Dietrich, Ruhr-University Bochum, Faculty of Mathematics,
Universita¨tsstr. 150, D-44780 Bochum, Germany;
e-mail: [email protected]
• Bruin, Marcel G. de, Delft University of Technology, Faculty of Electrical
Engineering, Mathematics and Computer Science, Department of Applied
Mathematics, Mekelweg 4, 2628 CD Delft, The Netherlands;
e-mail: [email protected]
• Bucci, Anthony, Brandis University, Computer Science Department,
Dynamical & Evolutionary Machine Organization,Waltham MA, U.S.A.;
e-mail: [email protected]
• Campiti, Michele, University of Lecce, Department of Mathematics ”E. De
Giorgi”, P.O. Box 193, I-73100 Lecce, Italy;
e-mail: [email protected]
• Catinas, Emil, Romanian Academy, Institute of Numerical Analysis, P.O.
Box 68-1, RO-3400 Cluj-Napoca, Romania
e-mail: [email protected]