Buch, Englisch, 352 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 717 g
ISBN: 978-0-8176-4702-5
Verlag: Birkhäuser Boston
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
- Mathematik | Informatik Mathematik Algebra Homologische Algebra
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
- Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik EDV | Informatik Informatik
- Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
Weitere Infos & Material
Shape-Preserving Approximation By Real Univariate Polynomials.- Shape-Preserving Approximation by Real Multivariate Polynomials.- Shape-Preserving Approximation by Complex Univariate Polynomials.- Shape-Preserving Approximation by Complex Multivariate Polynomials.- Appendix: Some Related Topics.
