Multivariate Polynomial Natural Splines for Interpolation of Scattered Data and Other Applications PDF Download
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Author: C. K. Chui
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 38
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Book Description
Based on the general Hilbert space theory of spline interpolation, multivariate natural polynomial spline functions are introduced as a generalization of the well-known univariate natural polynomial splines. Explicit formulations of these spline interpolants without boundary conditions to scattered data on certain bounded domains in R^s are constructed. It turns out that these new multivariate spline interpolants are fairly easy to implement and hence should be very useful in multivariate numerical analysis, such as numerical integrations and numerical solutions of partial differential equations.
Author: C. K. Chui
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 38
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Book Description
Based on the general Hilbert space theory of spline interpolation, multivariate natural polynomial spline functions are introduced as a generalization of the well-known univariate natural polynomial splines. Explicit formulations of these spline interpolants without boundary conditions to scattered data on certain bounded domains in R^s are constructed. It turns out that these new multivariate spline interpolants are fairly easy to implement and hence should be very useful in multivariate numerical analysis, such as numerical integrations and numerical solutions of partial differential equations.
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: 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: A Conte
Publisher: World Scientific
ISBN: 9814553700
Category :
Languages : en
Pages : 266
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Book Description
This volume focuses on the more recent results in computational geometry, such as algorithms for computer pictures of algebraic surfaces, the dimensionality paradigm and medial axis transform in geometric and solid modeling, stationary and non-stationary subdivision schemes for the generation of curves and surfaces, minimum norm networks in CAGD, knot removal and constrained knot removal for spline curves, blossoming in CAGD, triangulation methods, geometric modeling.
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: George Anastassiou
Publisher: CRC Press
ISBN: 0429525117
Category : Mathematics
Languages : en
Pages : 413
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Book Description
Working computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approximation theory-on the borderline between pure and applied mathematics- has always supplied some of the most innovative ideas, computational methods, and original approaches to many types of problems. The f
Author: Yuan Y. Tang
Publisher: Springer
ISBN: 3540453334
Category : Computers
Languages : en
Pages : 470
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Book Description
This book constitutes the refereed proceedings of the Second International Conference on Wavelet Analysis and Its Applications, WAA 2001, held in Hong Kong, China in December 2001. The 24 revised full papers and 27 revised short papers presented were carefully reviewed and selected from a total of 67 full paper submissions. The book offers topical sections on image compression and coding, video coding and processing, theory, image processing, signal processing, and systems and applications.
Author: Dominik Stahl
Publisher:
ISBN:
Category :
Languages : en
Pages : 108
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Book Description
Author: B.N. Sahney
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Proceedings of the NATO Advanced Study Institute, Calgary, Canada, August 26-September 2, 1978
Author: Ognyan Kounchev
Publisher: Academic Press
ISBN: 0080525008
Category : Mathematics
Languages : en
Pages : 513
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Book Description
Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate polysplines have applications in the design of surfaces and "smoothing" that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, polysplines are proving more effective than well-established methods, such as kKriging, radial basis functions, thin plate splines and minimum curvature. Part 1 assumes no special knowledge of partial differential equations and is intended as a graduate level introduction to the topic Part 2 develops the theory of cardinal Polysplines, which is a natural generalization of Schoenberg's beautiful one-dimensional theory of cardinal splines Part 3 constructs a wavelet analysis using cardinal Polysplines. The results parallel those found by Chui for the one-dimensional case Part 4 considers the ultimate generalization of Polysplines - on manifolds, for a wide class of higher-order elliptic operators and satisfying a Holladay variational property
