International Series of Numerical Mathematics

13 primary works

Funktionalanalysis Approximationstheorie Numerische Mathematik

by L Collatz, G. Meinardus, and H. Unger

Published 1 January 1967

Numerische Methoden Bei Optimierungsaufgaben

by L Collatz and W Wetterling

Published 1 January 1973

Numerische Methoden Bei Differentialgleichungen Und Mit Funktionalanalytischen Hilfsmitteln

by J. Albrecht and L Collatz

Published 1 January 1974

Numerische Behandlung Von Differentialgleichungen

by R. Ansorge, L Collatz, G Hammerlin, and W. Tornig

Published 1 January 1975

Numerische Methoden der Approximationstheorie/Numerical Methods of Approximation Theory

by Lothar Collatz, G. Meinardus, and H. Werner

Published 1 January 1976

Der vorliegende Band stellt Vortragsmanuskripte einer am Mathematischen Forschungsinstitut, Oberwolfach, in der Zeit vom 25. bis 31. Mai 1975 veran- stalteten Tagung zusammen, die unter der Leitung der Unterzeichner stand. Die letzten dieser Tagungen uber numerische Methoden der Approximations- theorie fanden 1971 und 1973 statt - der Schwerpunkt lag bei Fragen der Numerik von Algorithmen zur Darstellung von Funktionen -, liessen aber bereits ein wachsendes Interesse an Anwendungen erkennen. Die diesjahrige Tagung war gekennzeichnet durch die Behandlung praktischer AufgabensteI- lungen sowie durch die Einbeziehung der Anwendungen aus Nachbargebie- ten bzw. die Verwendung der Methoden dieser Gebiete in der Approxima- tionstheorie, insbesondere wurde auch auf die Beziehungen von Optimierung und Kontrolltheorie zu speziellen approximationstheoretischen Aufgaben eingegangen. Der starke Einfluss auf die numerischen Methoden zur Behand- lung von Differentialgleichungen wurde etwa bei der Methode der finiten Elemente oder bei Kollokationsaufgaben deutlich. So ist zu hoffen, dass auch diese Tagung dazu beigetragen hat, Theorie und Anwendungen wieder starker zu verbinden.
Die spezifische Atmosphare des Forschungsinstituts stimulierte einen intensi- ven, durch die breite internationale Streuung der Tagungsteilnehmer verstark- ten, fruchtbaren Gedankenaustausch. Zum Erfolg der Tagung trug - wie immer - die hervorragende Betreuung durch die Mitarbeiter und Angestellten des Forschungsinstituts und das verstandnisvolle Entgegenkommen von Herrn Kollege Barner bei. Unser besonderer Dank gilt ferner dem Birkhauser Verlag fur die sehr gute Ausstattung des Buches. L. COLLATZ, G. MEINARDUS, H. WERNER Inhaltsverzeichnis ANSELONE, P. M. , LEE, J. W. : Double Approximation Methods for the Solution of Fredholm Integral Equations ...

Numerische Methoden Bei Optimierungsaufgaben Band 3

by L Collatz, G. Meinardus, and W Wetterling

Published 1 January 1977

Konstruktive Methoden Der Finiten Nichtlinearen Optimierung

by Lothar Collatz, Gunther Meinardus, and Wolfgang Wetterling

Published 1 January 1980

Numerical Treatment of Free Boundary Value Problems / Numerische Behandlung Freier Randwertaufgaben

by J. Albrecht, Lothar Collatz, and K H Hoffmann

Published 1 January 1981

Differential-Difference Equations/Differential-Differenzengleichungen

by Lothar Collatz

Published 1 January 1983

Constructive Methods for the Practical Treatment of Integral Equations

by G Hammerlin and K H Hoffmann

Published 1 January 1985

O I 1 -1 durch die GauB-Quadraturformel Q I n n L w 0 f (x 0) * i=1 1 1 Sei Rn : = I - Q das Fehlerfunktional. n Izl1, Fur eine im Kreis Kr I Kr : = {z E a: holomorphe Funktion f, f(z) = L i=O sei f i i * = x . ( 1. 1) : = sup{ I a 0 I r i E:JN und R (qo) * O}, qo (x) o 1 n 1 1 In Xr := {f: f holomorph in Kr und Iflr oo} ist I . I eine Seminorm. Das Fehlerfunktional Rn ist in r (X I* I r) stetig I und fUr II Rn II I r, gilt die Identitat 00 (1 . 2) L i=O Dieser Zugang zu ableitungsfreien Abschatzungen des Fehlerterms (1 * 3) geht auf Hammerlin [4] zurUck. 15 Erftillt die Gewichtsfunktion w eine der Bedingungen w (t ) w(t ) 1 2;;; (1. 4. a) w (-t ) w (-t ) 1 2 beziehungsweise w (t ) w(t ) 1 2 (1. 4. b) ~ w (-t ) w (-t ) 1 2 so gilt mit P (x) (X-X ) *. * (X-X ) ftir die Fehlernorm 1 n n r 1 Pn(x) (1. 5. a) --,-. . - J w (x) dx Pn(r) -1 r-x beziehungsweise r 1 P (x) (1. 5. b) ( ) J w(x) ~ dx .

Delay Equations, Approximation and Application

by G. Meinardus and Gunther Nurnberger

Published 1 January 1985

The international symposium held in October 1984 at the Uni- versity of Mannheim was the first with the special aim to expose the connection of the Theory of Delay Eauations and Approximation Theory with the emphasis on constructive methods and applications. Although the separate character of both domains is reflected by their historical development, the latest research shows that the numerical treatment of Delay Equations leads to various appro- ximation and optimization problems. An introductory survey of this circle of problems written by the editors is included at the beginning of the book. Delay Equations have their origin in domains of applications, such as physics, engineering, biology, medicine and economics. They appear in connection with the fundamental problem to analyse a retarded process from the real world, to develop a corresponding mathematical model and to determine the future behavior. Thirty mathematicians attended the conference coming from Germany, West- and Eastern Europe and the United States- more than twenty of them presented a research talk.
The lectures about Delay Equations were mainly oriented on the following subjects: single-step, multi-step and spline methods; monotonicity methods for error estimations; asymptotic behavior 10 and periodicity of solutions. The topics of the talks on Approxi- mation Theory covered different aspects of approximation by poly- nomials, splines and rational functions and their numerical rea- lization. Additionally included in the scientific program was a special session on Open Problems, where several suggestions were made for further research concerning both fields.

Trends in Mathematical Optimization

by K H Hoffmann

Published 1 January 1987

This volume contains a collection of 23 papers presented at the 4th French-German Conference on Optimization, hold at Irsee, April 21 - 26, 1986. The conference was aUended by ninety scientists: about one third from France, from Germany and from third countries each. They all contributed to a highly interesting and stimulating meeting. The scientifique program consisted of four survey lectures of a more tutorical character and of 61 contributed papers covering almost all areas of optimization. In addition two informal evening sessions and a plenary discussion on further developments of optimization theory were organized. One of the main aims of the organizers was to indicate and to stress the increasing importance of optimization methods for almost all areas of science and for a fast growing number of industry branches. We hope that the conference approached this goal in a certain degree and managed to continue fruitful discussions between -theory and -applications-. Equally important to the official contributions and lectures is the -nonmeasurable part of activities inherent in such a scientific meeting. Here the charming and inspiring atmosphere of a place like Irsee helped to establish numerous new contacts between the participants and to deepen already existing ones. The conference was sponsored by the Bayerische Kultusministerium, the Deutsche Forschungsgemeinschaft and the Universities of Augsburg and Bayreuth. Their interest in the meeting and their assistance is gratefully acknowledged. We would like to thank the authors for their contributions and the referees for their helpful comments.

Numerical Treatment of Eigenvalue Problems / Numerische Behandlung von Eigenwertaufgaben

by J. Albrecht, Lothar Collatz, P. Hagedorn, and W. Velte

Published 1 March 1991