Numerical Methods of Approximation Theory, Vol.6 \ Numerische Methoden der Approximationstheorie, Band 6
Numerical Methods of Approximation Theory, Vol.6 \ Numerische Methoden der Approximationstheorie, Band 6

Author: Collatz

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 267

ISBN-13: 3034871864

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Der Band enthalt Manuskripte zu Vortragen, die auf einer von den Herausgebern geleiteten Tagung tiber "Numerische Methoden der Approximationstheorie" am Mathematischen Forschungsinstitut Ober wolfach in der Zeit vom 18.-24. Januar 1981 gehalten wurden. Das Spektrum der Vortrage reichte von der klassischen Approximations theorie tiber mehrdimensionale Approximationsverfahren bis hin zu praxisbezogenen Fragestellungen. Zu den zuerst genannten Gebieten gehorten z. B. die Verfeinerung von Fehlerabschatzungen bei der Polynominterpolation, Fragen zur Eindeutigkeit, Charakterisierung optimaler Interpolationsprozesse und Algorithmen zur rationalen Interpolation. Bei den weiteren genannten Gebieten spiegel ten zahlreiche Vortrage das steigende Interesse an der mehrdimensio nalen Interpolation, insbesondere mit verschiedenen Arten von Splines wider. Hier standen u. a. Probleme der Parameterschatzung in der Medizin und Flugtechnik, Fragen der Approximationstheorie bei der Konstruktion von Plottern und stabile Algorithmen beim Arbeiten mit mehrdimensionalen B-Splines im Mittelpunkt des Interesses. Die Tagung lieferte einen reprasentativen Ueberblick tiber die aktuellen Trends in der Approximationstheorie. Zum guten Erfolg der Tagung trug wie immer die hervorragende Be treuung durch die Mitarbeiter und Angestellten des Instituts so-' wie das verstandnisvolle Entgegenkommen des Institutsdirektors, Herrn Professor Dr. Barner, bei. Un serer besonderer Dank gilt dem Birkhauser Verlag ftir die wie stets sehr gute Ausstattung. Helmut Werner Lothar Collatz Gtinther Meinardus Hamburg Mannheim Bonn 7 INDEX Blatt, H.-P. Strenge Eindeutigkeitskonstanten und Fehlerabschatzungen bei linearer Tschebyscheff-Approximation 9 Bohmer, K. Polynom- und Spline-Interpolation (Ein Farbfilm) 26 Brannigan, M.A Multivariate Adaptive Data Fitting Algorithm 30 Brass, H. Zur numerischen Berechnung konjugierter Funktionen 43 Bultheel, A

Quantitative Approximation
Quantitative Approximation

Author: Ronald A. Devore

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 337

ISBN-13: 1483265129

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Quantitative Approximation provides information pertinent to nonlinear approximation, including rational approximation and optimal knot spline approximation. This book discusses spline approximation with the most emphasis on multivariate and knot independent questions. Organized into 26 chapters, this book begins with an overview of the inequality for the sharp function in terms of the maximal rearrangement. This text then examines the best co-approximation in a Hilbert space wherein the existence ad uniqueness sets are the closed flats. Other chapters consider the inverse of the coefficient matrix for the system satisfied by the B-spline coefficients of the cubic spline interpolant at knots. This book discusses as well the relationship between the structural properties of a function and its degree of approximation by rational functions. The final chapter deals with the problem of existence of continuous selections for metric projections and provides a solution for this problem. This book is a valuable resource for mathematicians.

Mathematical Programming The State of the Art
Mathematical Programming The State of the Art

Author: A. Bachem

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 662

ISBN-13: 3642688748

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In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most important fields of applied mathematics with extensive use in engineering, natural sciences, economics, and biological sciences. The lively activity in this area is demonstrated by the fact that as early as 1949 the first "Symposium on Mathe matical Programming" took place in Chicago. Since then mathematical programmers from all over the world have gath ered at the intfrnational symposia of the Mathematical Programming Society roughly every three years to present their recent research, to exchange ideas with their colleagues and to learn about the latest developments in their own and related fields. In 1982, the XI. International Symposium on Mathematical Programming was held at the University of Bonn, W. Germany, from August 23 to 27. It was organized by the Institut fUr Okonometrie und Operations Re search of the University of Bonn in collaboration with the Sonderforschungs bereich 21 of the Deutsche Forschungsgemeinschaft. This volume constitutes part of the outgrowth of this symposium and docu ments its scientific activities. Part I of the book contains information about the symposium, welcoming addresses, lists of committees and sponsors and a brief review about the Ful kerson Prize and the Dantzig Prize which were awarded during the opening ceremony.

Introduction to Numerical Continuation Methods
Introduction to Numerical Continuation Methods

Author: Eugene L. Allgower

Publisher: SIAM

Published: 2003-01-01

Total Pages: 413

ISBN-13: 9780898719154

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Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. The book also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals. To help potential users of numerical continuation methods create programs adapted to their particular needs, this book presents pseudo-codes and Fortran codes as illustrations. Since it first appeared, many specialized packages for treating such varied problems as bifurcation, polynomial systems, eigenvalues, economic equilibria, optimization, and the approximation of manifolds have been written. The original extensive bibliography has been updated in the SIAM Classics edition to include more recent references and several URLs so users can look for codes to suit their needs. Audience: this book continues to be useful for researchers and graduate students in mathematics, sciences, engineering, economics, and business. A background in elementary analysis and linear algebra are adequate prerequisites for reading this book; some knowledge from a first course in numerical analysis may also be helpful.

Curves and Surfaces
Curves and Surfaces

Author: Pierre-Jean Laurent

Publisher: Academic Press

Published: 2014-05-12

Total Pages: 535

ISBN-13: 1483263878

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Curves and Surfaces provides information pertinent to the fundamental aspects of approximation theory with emphasis on approximation of images, surface compression, wavelets, and tomography. This book covers a variety of topics, including error estimates for multiquadratic interpolation, spline manifolds, and vector spline approximation. Organized into 77 chapters, this book begins with an overview of the method, based on a local Taylor expansion of the final curve, for computing the parameter values. This text then presents a vector approximation based on general spline function theory. Other chapters consider a nonparametric technique for estimating under random censorship the amplitude of a change point in change point hazard models. This book discusses as well the algorithm for ray tracing rational parametric surfaces based on inversion and implicitization. The final chapter deals with the results concerning the norm of the interpolation operator and error estimates for a square domain. This book is a valuable resource for mathematicians.

Algorithms for Approximation
Algorithms for Approximation

Author: J. C. Mason

Publisher: Oxford University Press, USA

Published: 1987

Total Pages: 732

ISBN-13:

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The term "approximation" here refers to the approximation of functions and data by simple functions. Emphasizing the development of useful algorithms and practical applications in defense and industry, the papers cover topics such as multivariate interpolation, optimization methods, constrained problems, spline fitting, data modelling, and applications in microwave measurement, isotropic antennas, sound measurement, and digitized contours. Includes a substantial catalog of existing algorithms. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Numerical Continuation Methods
Numerical Continuation Methods

Author: Eugene L. Allgower

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 402

ISBN-13: 3642612571

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Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.

Computational Solution of Nonlinear Systems of Equations
Computational Solution of Nonlinear Systems of Equations

Author: Eugene L. Allgower

Publisher: American Mathematical Soc.

Published: 1990-04-03

Total Pages: 788

ISBN-13: 9780821896945

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Nonlinear equations arise in essentially every branch of modern science, engineering, and mathematics. However, in only a very few special cases is it possible to obtain useful solutions to nonlinear equations via analytical calculations. As a result, many scientists resort to computational methods. This book contains the proceedings of the Joint AMS-SIAM Summer Seminar, ``Computational Solution of Nonlinear Systems of Equations,'' held in July 1988 at Colorado State University. The aim of the book is to give a wide-ranging survey of essentially all of the methods which comprise currently active areas of research in the computational solution of systems of nonlinear equations. A number of ``entry-level'' survey papers were solicited, and a series of test problems has been collected in an appendix. Most of the articles are accessible to students who have had a course in numerical analysis.