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Synopsis
First comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables
Of interest to grad students and researchers in approximation theory, mathematical analysis, numerical analysis, Computer Aided Geometric Design, robotics, data fitting, chemistry, fluid mechanics, and engineering
Contains many open problems to spur future research
Rich and updated bibliography
"synopsis" may belong to another edition of this title.
From the Back Cover
This monograph presents the first comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables. Such approximation methods are useful in many problems that arise in science and engineering and require an optimal mathematical representation of physical reality.
The main topics are structured in four chapters, followed by an appendix: shape-preserving approximation and interpolation of real functions of one real variable by real polynomials; shape-preserving approximation of real functions of several real variables by multivariate real polynomials; shape-preserving approximation of analytic functions of one complex variable by complex polynomials in the unit disk; and shape-preserving approximation of analytic functions of several complex variables on the unit ball or the unit polydisk by polynomials of several complex variables. The appendix treats related results of non-polynomial and non-spline approximations preserving shape including those by complexified operators with applications to complex partial differential equations.
Shape-Preserving Approximation by Real and Complex Polynomials contains many open problems at the end of each chapter to stimulate future research along with a rich and updated bibliography surveying the vast literature. The text will be useful to graduate students and researchers interested in approximation theory, mathematical analysis, numerical analysis, computer aided geometric design, robotics, data fitting, chemistry, fluid mechanics, and engineering.
Review
From the reviews:
"This monograph is a rich collection of existing and new results in an important part of approximation theory, in which the object of approximation and the instrument for approximation share the same shape characteristics. ... This is convenient for a reference book ... . This book is a result of hard work and deep knowledge of the subject. It is a very important reference book for experts in approximation theory and would be a worthy addition to any mathematics library." (Bl. Sendov, Mathematical Reviews, Issue 2009 m)
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- PublisherBirkhäuser
- Publication date2008
- ISBN 10 0817647023
- ISBN 13 9780817647025
- BindingHardcover
- LanguageEnglish
- Number of pages365
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Shape- Preserving Approximation By Real And Complex Polynomials (Hb)
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Shape- Preserving Approximation By Real And Complex Polynomials (Hb)
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Shape-Preserving Approximation by Real and Complex Polynomials
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Shape-Preserving Approximation by Real and Complex Polynomials
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Shape-Preserving Approximation by Real and Complex Polynomials
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Shape-preserving Approximation By Real And Complex Polynomials
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Shape-preserving Approximation By Real And Complex Polynomials
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Shape-Preserving Approximation by Real and Complex Polynomials
Published by
Birkhäuser Boston Sep 2008, 2008
ISBN 10: 0817647023
ISBN 13: 9780817647025
New
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Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -First comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variablesOfinterest tograd students and researchers inapproximation theory, mathematical analysis, numerical analysis, Computer Aided Geometric Design, robotics, data fitting, chemistry, fluid mechanics, and engineeringContains many open problems to spur future researchRich and updated bibliography 368 pp. Englisch. Seller Inventory # 9780817647025
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Shape-Preserving Approximation by Real and Complex Polynomials
Seller: Buchpark, Trebbin, Germany
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Condition: Sehr gut. Zustand: Sehr gut | Seiten: 368 | Sprache: Englisch | Produktart: Bücher. Seller Inventory # 3966940/12
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Shape-Preserving Approximation by Real and Complex Polynomials
Published by
Birkhäuser Boston, Birkhäuser Boston, 2008
ISBN 10: 0817647023
ISBN 13: 9780817647025
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Hardcover
Seller: AHA-BUCH GmbH, Einbeck, Germany
Seller rating 5 out of 5 stars
Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - In many problems arising in engineering and science one requires approxi- tion methods to reproduce physical reality as well as possible. Very schema- cally, if the input data represents a complicated discrete/continuous quantity of information, of 'shape' S (S could mean, for example, that we have a 'monotone/convex' collection of data), then one desires to represent it by the less-complicated output information, that 'approximates well' the input data and, in addition, has the same 'shape' S. This kind of approximation is called 'shape-preserving approximation' and arises in computer-aided geometric design, robotics, chemistry, etc. Typically, the input data is represented by a real or complex function (of one or several variables), and the output data is chosen to be in one of the classes polynomial, spline, or rational functions. The present monograph deals in Chapters 1-4 with shape-preserving - proximation by real or complex polynomials in one or several variables. Chapter 5 is an exception and is devoted to some related important but n- polynomial andnonsplineapproximations preservingshape.Thesplinecaseis completely excluded in the present book, since on the one hand, many details concerning shape-preserving properties of splines can be found, for example, in the books of de Boor [49], Schumaker [344], Chui [69], DeVore-Lorentz [91], Kvasov [218] and in the surveys of Leviatan [229], Koci c-Milovanovi c [196], while on the other hand, we consider that shape-preserving approximation by splines deserves a complete study in a separate book. Seller Inventory # 9780817647025
Quantity: 1 available