Applications of Spline Functions in Economics PDF Download
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Author: Dale J. Poirier
Publisher:
ISBN:
Category : Econometrics
Languages : en
Pages : 454
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Book Description
Author: Dale J. Poirier
Publisher:
ISBN:
Category : Econometrics
Languages : en
Pages : 454
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Book Description
Author: Thomas Nall Eden Greville
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 232
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Book Description
Author: Larry Schumaker
Publisher: Cambridge University Press
ISBN: 1139463438
Category : Mathematics
Languages : en
Pages : 524
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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
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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: Serge Dubuc
Publisher: American Mathematical Soc.
ISBN: 0821808753
Category : Mathematics
Languages : en
Pages : 409
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Book Description
This work is based on a series of thematic workshops on the theory of wavelets and the theory of splines. Important applications are included. The volume is divided into four parts: Spline Functions, Theory of Wavelets, Wavelets in Physics, and Splines and Wavelets in Statistics. Part one presents the broad spectrum of current research in the theory and applications of spline functions. Theory ranges from classical univariate spline approximation to an abstract framework for multivariate spline interpolation. Applications include scattered-data interpolation, differential equations and various techniques in CAGD. Part two considers two developments in subdivision schemes; one for uniform regularity and the other for irregular situations. The latter includes construction of multidimensional wavelet bases and determination of bases with a given time frequency localization. In part three, the multifractal formalism is extended to fractal functions involving oscillating singularites. There is a review of a method of quantization of classical systems based on the theory of coherent states. Wavelets are applied in the domains of atomic, molecular and condensed-matter physics. In part four, ways in which wavelets can be used to solve important function estimation problems in statistics are shown. Different wavelet estimators are proposed in the following distinct cases: functions with discontinuities, errors that are no longer Gaussian, wavelet estimation with robustness, and error distribution that is no longer stationary. Some of the contributions in this volume are current research results not previously available in monograph form. The volume features many applications and interesting new theoretical developments. Readers will find powerful methods for studying irregularities in mathematics, physics, and statistics.
Author: Borislav D. Bojanov
Publisher: Springer
ISBN: 9780792322290
Category : Computers
Languages : en
Pages : 292
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Book Description
This volume provides a comprehensive introduction to the theory of spline functions. Emphasis is given to new developments, such as the general Birkhoff-type interpolation, the extremal properties of splines, their prominent role in the optimal recovery of functions, and multivariate interpolation by polynomials and splines. The book has thirteen chapters dealing, respectively, with interpolation by algebraic polynomials, the space of splines, B-splines, interpolation by spline functions, natural spline functions, perfect splines, monosplines, periodic splines, multivariate B-splines and truncated powers, multivariate spline functions and divided differences, box splines, multivariate mean value interpolation, multivariate polynomial interpolations arising by hyperplanes, and multivariate pointwise interpolation. Some of the results described are presented as exercises and hints are given for their solution. For researchers and graduate students whose work involves approximation theory.
Author: Gheorghe Micula
Publisher: Springer Science & Business Media
ISBN: 9401153388
Category : Mathematics
Languages : en
Pages : 622
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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: Borislav D. Bojanov
Publisher: Springer Science & Business Media
ISBN: 940158169X
Category : Mathematics
Languages : en
Pages : 287
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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: Thomas Nall Eden Greville
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 107
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Book Description
The document begins with a definition of a spline function, some general remarks about the nature and uses of such functions, an illustrative example, and a simple algebraic representation for any spline function. The important subclass of natural splines is defined in chapter 2 and the theorem of unique interpolation by natural splines and the well known minimal property of the smoothest interpolating natural spline is proven. Chapter 3 is concerned with the approximation of linear functionals. It includes Peano's theorem on remainders, A. Sard's theory of best approximation of linear functionals, and I.J. Schoenberg's discovery that finding the best approximation to a given functional in Sard's sense is equivalent to applying the functional to the corresponding natural spline interpolating function. Chapter 4 develops the properties of divided differences and of the B-splines, a special type of spline functions with limited support that constitute a basis for the class of spline functions and are important for computational purposes. Chapter 5 concerns a numerical algorithm for obtaining the natural spline interpolating function and also considers the smoothing natural splines resulting from Schoenberg's adaptation of E.T. Whittaker's smoothing method. (Author).
Author: Dale J. Poirier
Publisher: North-Holland
ISBN:
Category : Business & Economics
Languages : en
Pages : 224
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Book Description
An introduction to models of structural change; Linear splines; Cubic splines; Bilineart splines; Cobb-Douglas splines; Splines lags: why the almon lag has gone to pieces; A survey of estimation techniques for models with unknown points of structural change; The use of splines in multiple regression; Spline loss functions.
