Author : S. B. Stechkin
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 26,43 MB
Release : 1981
Category : Mathematics
ISBN : 9780821830499
Papers and articles about polynomials and splines pproximation.
Author : Albert Y. Zomaya
Publisher : Springer
Page : 0 pages
File Size : 44,2 MB
Release : 2008-11-01
Category : Computers
ISBN : 9780387516189
As computing devices proliferate, demand increases for an understanding of emerging computing paradigms and models based on natural phenomena. Neural networks, evolution-based models, quantum computing, and DNA-based computing and simulations are all a necessary part of modern computing analysis and systems development. Vast literature exists on these new paradigms and their implications for a wide array of applications. This comprehensive handbook, the first of its kind to address the connection between nature-inspired and traditional computational paradigms, is a repository of case studies dealing with different problems in computing and solutions to these problems based on nature-inspired paradigms. The "Handbook of Nature-Inspired and Innovative Computing: Integrating Classical Models with Emerging Technologies" is an essential compilation of models, methods, and algorithms for researchers, professionals, and advanced-level students working in all areas of computer science, IT, biocomputing, and network engineering.
Author : Klaus Hollig
Publisher : SIAM
Page : 228 pages
File Size : 12,10 MB
Release : 2015-07-01
Category : Mathematics
ISBN : 1611972949
B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.
Author : George M. Phillips
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 34,70 MB
Release : 2006-04-06
Category : Mathematics
ISBN : 0387216820
In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. The author is well known for his clarity of writing and his many contributions as a researcher in approximation theory.
Author : Theodore J. Rivlin
Publisher : Courier Corporation
Page : 164 pages
File Size : 41,77 MB
Release : 1981-01-01
Category : Mathematics
ISBN : 9780486640693
Mathematics of Computing -- Numerical Analysis.
Author : Ming-Jun Lai
Publisher : Cambridge University Press
Page : 28 pages
File Size : 25,76 MB
Release : 2007-04-19
Category : Mathematics
ISBN : 0521875927
Comprehensive graduate text offering a detailed mathematical treatment of polynomial splines on triangulations.
Author : M. J. D. Powell
Publisher : Cambridge University Press
Page : 356 pages
File Size : 15,61 MB
Release : 1981-03-31
Category : Mathematics
ISBN : 9780521295147
Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.
Author : Sorin G. Gal
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 29,51 MB
Release : 2010-06-09
Category : Mathematics
ISBN : 0817647031
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
Author : Larry Schumaker
Publisher : Cambridge University Press
Page : 524 pages
File Size : 15,81 MB
Release : 2007-08-16
Category : Mathematics
ISBN : 1139463438
This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.
Author : Borislav D. Bojanov
Publisher : Springer Science & Business Media
Page : 287 pages
File Size : 38,67 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 940158169X
Spline functions entered Approximation Theory as solutions of natural extremal problems. A typical example is the problem of drawing a function curve through given n + k points that has a minimal norm of its k-th derivative. Isolated facts about the functions, now called splines, can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J. Favard, L. Tschakaloff. However, the Theory of Spline Functions has developed in the last 30 years by the effort of dozens of mathematicians. Recent fundamental results on multivariate polynomial interpolation and multivari ate splines have initiated a new wave of theoretical investigations and variety of applications. The purpose of this book is to introduce the reader to the theory of spline functions. The emphasis is given to some new developments, such as the general Birkoff's type interpolation, the extremal properties of the splines and their prominant role in the optimal recovery of functions, multivariate interpolation by polynomials and splines. The material presented is based on the lectures of the authors, given to the students at the University of Sofia and Yerevan University during the last 10 years. Some more elementary results are left as excercises and detailed hints are given.
