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Author: Larry Schumaker Publisher: Cambridge University Press ISBN: 1139463438 Category : Mathematics Languages : en Pages : 524
Book Description
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: Larry Schumaker Publisher: Cambridge University Press ISBN: 1139463438 Category : Mathematics Languages : en Pages : 524
Book Description
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: J. H. Ahlberg Publisher: Elsevier ISBN: 1483222950 Category : Mathematics Languages : en Pages : 297
Book Description
The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.
Author: Borislav D. Bojanov Publisher: Springer Science & Business Media ISBN: 940158169X Category : Mathematics Languages : en Pages : 287
Book Description
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.
Author: Gheorghe Micula Publisher: Springer Science & Business Media ISBN: 9401153388 Category : Mathematics Languages : en Pages : 622
Book Description
The purpose of this book is to give a comprehensive introduction to the theory of spline functions, together with some applications to various fields, emphasizing the significance of the relationship between the general theory and its applications. At the same time, the goal of the book is also to provide new ma terial on spline function theory, as well as a fresh look at old results, being written for people interested in research, as well as for those who are interested in applications. The theory of spline functions and their applications is a relatively recent field of applied mathematics. In the last 50 years, spline function theory has undergone a won derful development with many new directions appearing during this time. This book has its origins in the wish to adequately describe this development from the notion of 'spline' introduced by 1. J. Schoenberg (1901-1990) in 1946, to the newest recent theories of 'spline wavelets' or 'spline fractals'. Isolated facts about the functions now called 'splines' can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J.
Author: Albert Y. Zomaya Publisher: Springer ISBN: 9780387516189 Category : Computers Languages : en Pages : 0
Book Description
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: Grace Wahba Publisher: SIAM ISBN: 0898712440 Category : Mathematics Languages : en Pages : 174
Book Description
This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework. Methods for including side conditions and other prior information in solving ill posed inverse problems are provided. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.
Author: Klaus Hollig Publisher: SIAM ISBN: 1611972949 Category : Mathematics Languages : en Pages : 228
Book Description
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: P. M. Prenter Publisher: Courier Corporation ISBN: 0486469026 Category : Mathematics Languages : en Pages : 338
Book Description
One of the clearest available introductions to variational methods, this text requires only a minimal background in linear algebra and analysis. It explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. Many helpful definitions, examples, and exercises appear throughout the book. 1975 edition.
Author: Larry Schumaker
Author: Larry Schumaker
Author: Larry L. Schumaker
Author: J. H. Ahlberg
Author: Ming-Jun Lai
Author: Borislav D. Bojanov
Author: Gheorghe Micula
Author: Albert Y. Zomaya
Author: Grace Wahba
Author: Klaus Hollig
Author: P. M. Prenter