Spline Functions And Multivariate Interpolations

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Spline Functions and Multivariate Interpolations

Author : Borislav D. Bojanov
Publisher : Springer Science & Business Media
ISBN 13 : 940158169X
Total Pages : 287 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Spline Functions and Multivariate Interpolations by : Borislav D. Bojanov

Download or read book Spline Functions and Multivariate Interpolations written by Borislav D. Bojanov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spline Functions and Multivariate Interpolations

Author : Borislav D. Bojanov
Publisher : Springer
ISBN 13 : 9780792322290
Total Pages : 292 pages
Book Rating : 4.3/5 (222 download)

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Book Synopsis Spline Functions and Multivariate Interpolations by : Borislav D. Bojanov

Download or read book Spline Functions and Multivariate Interpolations written by Borislav D. Bojanov and published by Springer. This book was released on 1993-03-31 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multivariate Approximation and Splines

Author : Günther Nürnberger
Publisher : Birkhäuser
ISBN 13 : 3034888716
Total Pages : 329 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Multivariate Approximation and Splines by : Günther Nürnberger

Download or read book Multivariate Approximation and Splines written by Günther Nürnberger and published by Birkhäuser. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the refereed papers which were presented at the interna tional conference on "Multivariate Approximation and Splines" held in Mannheim, Germany, on September 7-10,1996. Fifty experts from Bulgaria, England, France, Israel, Netherlands, Norway, Poland, Switzerland, Ukraine, USA and Germany participated in the symposium. It was the aim of the conference to give an overview of recent developments in multivariate approximation with special emphasis on spline methods. The field is characterized by rapidly developing branches such as approximation, data fit ting, interpolation, splines, radial basis functions, neural networks, computer aided design methods, subdivision algorithms and wavelets. The research has applications in areas like industrial production, visualization, pattern recognition, image and signal processing, cognitive systems and modeling in geology, physics, biology and medicine. In the following, we briefly describe the contents of the papers. Exact inequalities of Kolmogorov type which estimate the derivatives of mul the paper of BABENKO, KOFANovand tivariate periodic functions are derived in PICHUGOV. These inequalities are applied to the approximation of classes of mul tivariate periodic functions and to the approximation by quasi-polynomials. BAINOV, DISHLIEV and HRISTOVA investigate initial value problems for non linear impulse differential-difference equations which have many applications in simulating real processes. By applying iterative techniques, sequences of lower and upper solutions are constructed which converge to a solution of the initial value problem.

Multivariate Splines

Author : Charles K. Chui
Publisher : SIAM
ISBN 13 : 0898712262
Total Pages : 192 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Multivariate Splines by : Charles K. Chui

Download or read book Multivariate Splines written by Charles K. Chui and published by SIAM. This book was released on 1988-01-01 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subject of multivariate splines presented from an elementary point of view; includes many open problems.

Topics in Multivariate Approximation

Author : C. K. Chui
Publisher : Elsevier
ISBN 13 : 1483271005
Total Pages : 346 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Topics in Multivariate Approximation by : C. K. Chui

Download or read book Topics in Multivariate Approximation written by C. K. Chui and published by Elsevier. This book was released on 2014-05-10 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Multivariate Approximation contains the proceedings of an international workshop on multivariate approximation held at the University of Chile in Santiago, Chile, on December 15-19, 1986. Leading researchers in the field discussed several problem areas related to multivariate approximation and tackled topics ranging from multivariate splines and fitting of scattered data to tensor approximation methods and multivariate polynomial approximation. Numerical grid generation and finite element methods were also explored, along with constrained interpolation and smoothing. Comprised of 22 chapters, this book first describes the application of Boolean methods of approximation in combination with the theory of right invertible operators to bivariate Fourier expansions. The reader is then introduced to ill-posed problems in multivariate approximation; interpolation of scattered data by radial functions; and shape-preserving surface interpolation. Subsequent chapters focus on approximation by harmonic functions; numerical generation of nested series of general triangular grids; triangulation methods; and inequalities arising from best local approximations in rectangles. A bibliography of multivariate approximation concludes the book. This monograph will be of interest to mathematicians.

Smoothing and Multivariate Interpolation with Splines

Author : T. L. Jordan
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Smoothing and Multivariate Interpolation with Splines by : T. L. Jordan

Download or read book Smoothing and Multivariate Interpolation with Splines written by T. L. Jordan and published by . This book was released on 1965 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topics in Multivariate Approximation and Interpolation

Author : Kurt Jetter
Publisher : Elsevier
ISBN 13 : 0080462049
Total Pages : 357 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Topics in Multivariate Approximation and Interpolation by : Kurt Jetter

Download or read book Topics in Multivariate Approximation and Interpolation written by Kurt Jetter and published by Elsevier. This book was released on 2005-11-15 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for graduate students specializing in these topics, and for researchers in universities and in industry. - A collection of articles of highest scientific standard - An excellent introduction and overview of recent topics from multivariate approximation - A valuable source of references for specialists in the field - A representation of the state-of-the-art in selected areas of multivariate approximation - A rigorous mathematical introduction to special topics of interdisciplinary research

Multivariate Polynomial Natural Splines for Interpolation of Scattered Data and Other Applications

Author : C. K. Chui
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.:/5 (16 download)

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Book Synopsis Multivariate Polynomial Natural Splines for Interpolation of Scattered Data and Other Applications by : C. K. Chui

Download or read book Multivariate Polynomial Natural Splines for Interpolation of Scattered Data and Other Applications written by C. K. Chui and published by . This book was released on 1990 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Polynomial and Spline Approximation

Author : B.N. Sahney
Publisher : Springer
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.:/5 (5 download)

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Book Synopsis Polynomial and Spline Approximation by : B.N. Sahney

Download or read book Polynomial and Spline Approximation written by B.N. Sahney and published by Springer. This book was released on 1979-05-31 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Calgary, Canada, August 26-September 2, 1978

Interpolation and Approximation with Splines and Fractals

Author : Peter Robert Massopust
Publisher :
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Interpolation and Approximation with Splines and Fractals by : Peter Robert Massopust

Download or read book Interpolation and Approximation with Splines and Fractals written by Peter Robert Massopust and published by . This book was released on 2010 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and fractal surfaces. This synthesis will complement currently required courses dealing with these topics and expose the prospective reader to some new and deep relationships. In addition to providing a classical introduction to the main issues involving approximation and interpolation with uni- and multivariate splines, cardinal and exponential splines, and their connection to wavelets and multiscale analysis, which comprises the first half of the book, the second half will describe fractals, fractal functions and fractal surfaces, and their properties. This also includes the new burgeoning theory of superfractals and superfractal functions. The theory of splines is well-established but the relationship to fractal functions is novel. Throughout the book, connections between these two apparently different areas will be exposed and presented. In this way, more options are given to the prospective reader who will encounter complex approximation and interpolation problems in real-world modeling. Numerous examples, figures, and exercises accompany the material.

Multivariate Approximation and Interpolation

Author : HAUSMANN
Publisher : Springer-Verlag
ISBN 13 : 3034856857
Total Pages : 331 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Multivariate Approximation and Interpolation by : HAUSMANN

Download or read book Multivariate Approximation and Interpolation written by HAUSMANN and published by Springer-Verlag. This book was released on 2013-11-21 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Cardinal Spline Interpolation

Author : I. J. Schoenberg
Publisher : SIAM
ISBN 13 : 9781611970555
Total Pages : 131 pages
Book Rating : 4.9/5 (75 download)

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Book Synopsis Cardinal Spline Interpolation by : I. J. Schoenberg

Download or read book Cardinal Spline Interpolation written by I. J. Schoenberg and published by SIAM. This book was released on 1973-01-01 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: As this monograph shows, the purpose of cardinal spline interpolation is to bridge the gap between the linear spline and the cardinal series. The author explains cardinal spline functions, the basic properties of B-splines, including B- splines with equidistant knots and cardinal splines represented in terms of B-splines, and exponential Euler splines, leading to the most important case and central problem of the book-- cardinal spline interpolation, with main results, proofs, and some applications. Other topics discussed include cardinal Hermite interpolation, semi-cardinal interpolation, finite spline interpolation problems, extremum and limit properties, equidistant spline interpolation applied to approximations of Fourier transforms, and the smoothing of histograms.

Spline Functions

Author : Larry L. Schumaker
Publisher : SIAM
ISBN 13 : 1611973902
Total Pages : 420 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Spline Functions by : Larry L. Schumaker

Download or read book Spline Functions written by Larry L. Schumaker and published by SIAM. This book was released on 2015-01-01 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes in detail the key algorithms needed for computing with spline functions and illustrates their use in solving several basic problems in numerical analysis, including function approximation, numerical quadrature, data fitting, and the numerical solution of PDE's. The focus is on computational methods for bivariate splines on triangulations in the plane and on the sphere, although both univariate and tensor-product splines are also discussed. The book contains numerous examples and figures to illustrate the methods and their performance. All of the algorithms in the book have been coded in a separate MATLAB package available for license. The package can be used to run all of the examples in the book and also provides readers with the essential tools needed to create software for their own applications. In addition to the included bibliography, a list of over 100 pages of additional references can be found on the book's website.

Studies in Spline Functions and Approximation Theory

Author : Samuel Karlin
Publisher :
ISBN 13 :
Total Pages : 520 pages
Book Rating : 4.:/5 (5 download)

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Book Synopsis Studies in Spline Functions and Approximation Theory by : Samuel Karlin

Download or read book Studies in Spline Functions and Approximation Theory written by Samuel Karlin and published by . This book was released on 1976 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reports a series of research investigations concerned with spline functions and approximation theory. The common thread of the studies derives from the facts that (1) the subject matter of the individual articles relate and significantly complement each other; 92) part of the genesis and certainly the main developments of these studies occurred at the Weizmann Institute of Science, Rehovot, Israel, commencing about September 1970 through June 1974. The contributions cover aspects of the theory of best approximation and quadratures, the solution of certain extremal problems embracing generalized Landau and Markov-type inequalities for derivative functionals, and a hierarchy of interpolation and convergence properties of classes of spline functions.

Theory and Applications of Spline Functions

Author : Thomas Nall Eden Greville
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Theory and Applications of Spline Functions by : Thomas Nall Eden Greville

Download or read book Theory and Applications of Spline Functions written by Thomas Nall Eden Greville and published by . This book was released on 1969 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Splines

Author : Gheorghe Micula
Publisher : Springer Science & Business Media
ISBN 13 : 9401153388
Total Pages : 622 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Handbook of Splines by : Gheorghe Micula

Download or read book Handbook of Splines written by Gheorghe Micula and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spline Functions: Basic Theory

Author : Larry Schumaker
Publisher : Cambridge University Press
ISBN 13 : 1139463438
Total Pages : 524 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Spline Functions: Basic Theory by : Larry Schumaker

Download or read book Spline Functions: Basic Theory written by Larry Schumaker and published by Cambridge University Press. This book was released on 2007-08-16 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.