Multivariate Approximation and Interpolation: Proceedings of an International Workshop held at the University of Duisburg, August 14–18, 1989

331 Pages·1990·9.21 MB·German

by  Yu. A. Brudnyi (auth.)

ISNM94:
International Series of Numerical Mathematics
Internationale Schriftenreihe zur Numerischen Mathematik
Serie Internationale d'Analyse Numerique
VoI. 94
Edited by
K.-H. Hoffmann, Augsburg; H. D. Mittelmann, Tempe;
J. Todd, Pasadena
Birkhäuser Verlag
Basel· Boston· Berlin
Multivariate
Approximation
and Interpolation
Proceedings ofan InternationalWorkshop
held at the University ofDuisburg,
August 14-18,1989
Edited by
W.Haußmann
K. Jetter
1990 Springer Basel AG
Editors
W.Haußmann
K.Jetter
Fachgebiet Angewandte Analysis
FBMathematik
UniversitätDuisburg
D-4100Duisburg 1
IllustrationonpageVIII
withpermission ofthe Reg.-Präs.Düsseldorf(BRD)
LibraryofCongress CataloginginPublicationData
Multivariateapproximationandinterpolation:proceedingsofan
internationalworkshop heldatthe UniversityofDuisburg,
August 14-18,19891editedbyW.Haußmann, K.Jetter.
p. cm. - - (Internationalseriesofnumerical mathematics;
vol.94= Internationale SchriftenreihezurNumerischenMathematik:
vol.94= Serieinternationaled'analysenumerique;vol.94)
»TheInternationalWorkshoponMultivariateApproximationand
Interpolation« - - Pref.
0817624503(alk.paper)
1.Approximationtheory -- Congresses. 2.Interpolation --
Congresses. I. Haußmann,W.(Werner),1941- 1I.Jetter,K.
Ill.InternationalWorkshoponMultivariate Approximationand
Interpolation(1989 : UniversityofDuisburg) IV.Series:
Internationalseriesofnumerical mathematics ; v.94.
QA297.5.M843 1990
519.5'3 - - dc20
DeutscheBibliothekCataloguing-in-PublicationData
Multivariateapproximationandinterpolation: proceedingsof
aninternationalworkshop heldatthe University ofDuisburg,
August 14-18,19891ed.byW. Haußmann;K.Jetter.- Basel
Boston ; Berlin : Birkhäuser, 1990
(Internationalseriesofnumerical mathematics ; Vol.94)
NE:Haußmann,Werner[Hrsg.];Universität <Duisburg,1980->;GT
Thisworkissubject tocopyright. Allrightsare reserved,whetherthe wholeorpart
ofthe material isconcerned,specificallythose oftranslation,reprinting,re-useof
illustrations,broadcasting,reproductionbyphotocopyingmachineorsimilarmeans,
andstorage indata banks. Under§54ofthe GermanCopyright Lawwherecopiesare
madeforotherthan privateuseafeeispayable to»VerwertungsgesellschaftWort«,Munich.
ISBN 978-3-0348-5686-7 ISBN 978-3-0348-5685-0 (eBook)
DOI 10.1007/978-3-0348-5685-0
© 1990SpringerBaselAG
OriginallypublishedbyBirkhäuserVerlag,Baselin1990.
SoftcoverreprintofthehardcoverIstedition1990
v
Contents
Preface Vll
List of Participants ix
Scientific Program xiii
Adaptive approximation of functions with singularities
Yu. A. Brudnyi 1
Construction and applications ofinterpolation formulas
C. K. Chui 11
Asymptotic nonparametricspline density estimation in several
variables
Z. Ciesie1ski 25
On some recent methodsfor bivariate shape-preserving
interpolation
P. Costantini 55
On stationary subdivision and the construction of compactly
supported orthonormalwavelets
W. Dahmen and C. A. Micchelli 69
Interpolating subdivision schemes for the generation
of curves and surfaces
N. Dyn and D. Levin 91
Approximation of scattered data for meteorological applications
R. Franke 107
Some application of approximation theory to the first boundary
value problem of elastostatics
W. Freeden 121
Approximation by solutions of elliptic boundary value problems
U. Hamann and G. Wildenhain 131
Gn-l-functional splines for interpolation and approximation
of surfaces and solids
J. Hoschek, E. Hartmann,J.G. Li, and Y.Y.Feng 141
Lower bounds on the dimension of spaces of bivariate splines
R.Q.Jia 155
The use of homogeneous coordinates in spline functions and
polynomial interpolation
S. L. Lee 167
An efficient algorithm for Ck-simplicial finite element
interpolation in lRd
A. Le Mehaute 179
vi
On ridge-type functions with elliptie eontour lines
B. Lenze and F. Locher ............................................... 193
Polyharmonie splines, multiseale analysis, and entire functions
W. Madych 205
On the exponential eigen splines:Type-2 triangulation
H. ier Morsche 217
Univariate multiquadrie approximation: Reproduction of
linear polynomials
M. J. D. Powell 227
Uniform approximation of eontinuous functions with values in [0,1]
J. B. Prolla 241
Nonproduct interpolation and approximation
M. Reimer 249
Multivariate splines and dimensions of kernels oflinear operators
S. D. Riemenschneider, R. Q. Jia, and Z. Shen 261
Elliptie regularity with eontinuous and branehing edge asymptoties
B.-W. Schulze 275
Fast algorithms for one- and two-dimensional diserete
eosine transforms
G. Steidl and M. Tasche 285
Reeent results on multivariate smoothingsplines
F.I. Utreras 299
The obstacle problem and best superharmonieapproximation
D. Zwick 313
vii
Preface
The "International Workshop on Multivariate Approximation and Interpolation"
was held at the University of Duisburg, Germany, during August 14-18, 1989. It was
the second workshop in aseries which started in 1986 at the University of Chile in
Santiago with a previous conference on a similar subject (cf. Topics in Multivariate
Approximation, C.K. Chui et al. (Eds.), Academic Press, New York, 1987).
The conference was organizedby an international organizing committeeconsisting
of Charles Chui (USA), Werner Haußmann (Germany), Kurt Jetter (Germany), Larry
Schumaker (USA), and Florencio Utreras (Chile). In addition, the local organizing
committeeincluded Hans-BerndKnoop,Hauke Krüger, and JoachimStöcklerfrom the
University of Duisburg. We would like to thank all of them for their constant support.
We also acknowledge the efforts of Uta Dick, Sabine Häußler, and Stefanie Messal who
did most of the secretarial work.
It wasour pleasure to seethat the workshopbroughttogether 75participants from
18 countries. 28 leading scientists gave invited (research or survey) lectures, with 24
of them summarized in the papers included in this proceedings volume. The topics
of these lectures gave a state-of-the-art overview of current research in Multivariate
Approximationand Interpolation, and they reflected the rapid developmentofthearea.
In particular, the following subjects were covered:
- applications of cardinal interpolation
- approximation with solutions of PDE's
- Fast Fourier Transform methods
- fitting ofscattered data
- multivariate polynomial approximation
- multivariate splines
- numericalgrid generation
- radial basis funetions
- smoothingby splines,
We would like to thank the following institutions for financial support:University
of Duisburg, Deutsche Forschungsgemeinschaft (Bonn), US Navy - European Officeof
Naval Research (London), Bundesministerium für Innerdeutsche Beziehungen (Bonn),
Deutsche Stiftung für Internationale Entwicklung (Bonn), Deutscher Akademischer
Austauschdienst (Bonn), Unsere Duisburger Hochschule e.V. (Duisburg), and Thyssen
AG (Duisburg). Thanks are also due to the University of Duisburg for providing the
excellent conference site, and for technical assistance.
viii
The manuscript of this volume was prepared at the University of Duisburg using
the 'IEX-typesetting system.It was a great help that wewere allowed to use the macros
of the Center of Approximation Theory in College Station, Texas, which wegratefully
acknowledge. StefanieMessal assisted usin retypingseveral papers.Hans-BerndKnoop
and, in particular, Joachim Stöckler did an excellent job in getting the final form of
this volume. Last not least, we would like to express our thanks to Birkhäuser-Verlag,
Basel,for the efficient and smooth cooperation.
Duisburg, March 1990 The Editors
Werner Haußmann
Kurt Jetter
ix
List ofParticipants
G. BASZENSKI, Rechenzentrum, Ruhr-Universität Bochum, Universitätsstr. 150,4630
Bochum1, West Germany
M. BENNINGHOFF-GRASNICK,FachbereichMathematik,Universität Duisburg,Lothar
str. 65, 4100 Duisburg 1, West Germany
A. Boos, Fachbereich Mathematik, Universität Duisburg, Lotharstr. 65, 4100 Duis
burg 1, West Germany
M. BOZZINI, Via Vigäno 8, Milano, Italy
D. BRAESS, Fakultät für Mathematik, Ruhr-Universität Bochum,Universitätsstr. 150,
4630 Bochum1, West Germany
Yu. A. BRUDNYI, 150000 Yaroslavl', ul. Sovetskaya 14, State University, SSSR
E.-J. BÜSSE, GMD, Inst. f. Methodische Grundlagen ( F1 / T ), Postfach 1240, 5205
St. Augustin, West Germany
H.-G. BUHL, Fachbereich Mathematik der Bergischen Universität, Gaußstr. 20, 5600
Wuppertal1, West Germany
M. BUHMANN, DAMPT, University of Cambridge, Silver St., Cambridge CB3 9EW,
England
J. M. CARNICER,Depto. deMatematicaAplicada, Edificio deMatematicas, Plantal.a,
50009 Zaragoza, Spain
C. K. CHUI, Dept. of Mathematics, Texas A & M University, College Station, TX
77843, USA
Z. CIESIELSKI, Math. Inst. PAN, ul. Abrahama18,81-825 Sopot, Poland
P. COSTANTINI, Universita di Siena, Dipartimento di Matematica, Via del Capitano
15, 53100 Siena, Italy
C. COTTIN,Fachbereich Mathematik, Universität Duisburg, Lotharstr. 65, 4100 Duis
burg 1, West Germany
L. COTTIN,INFORMGmbH,GroßenbaumerWeg5,4000Düsseldorf30,West Germany
W. DAHMEN, Institut für Mathematik III, Freie Universität Berlin, Arnimallee 2-6,
1000 Berlin 33, West Germany
F.-J. DELVOS,FachbereichMathematik,Universität Siegen, Hölderlinstr.3,5900Siegen
21, West Germany
J. DONIG, Fachbereich Mathematik, Universität Duisburg, Lotharstr. 65, 4100 Duis
burg 1, West Germany
N. DYN,School ofMathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel
M. ECK, Fachbereich Mathematik, Techn. Hochschule Darmstadt, Schloßgartenstr. 7,
6100 Darmstadt, West Germany