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Author : Thomas Nall Eden Greville
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.3/5 (91 download)
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:
Author : J. H. Ahlberg
Publisher : Elsevier
ISBN 13 : 1483222950
Total Pages : 296 pages
Book Rating : 4.4/5 (832 download)
Download or read book The Theory of Splines and Their Applications written by J. H. Ahlberg and published by Elsevier. This book was released on 2016-06-03 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Larry Schumaker
Publisher : Cambridge University Press
ISBN 13 : 1139463438
Total Pages : 524 pages
Book Rating : 4.1/5 (394 download)
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.
Author : Borislav D. Bojanov
Publisher : Springer Science & Business Media
ISBN 13 : 940158169X
Total Pages : 287 pages
Book Rating : 4.4/5 (15 download)
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.
Author : Gheorghe Micula
Publisher : Springer Science & Business Media
ISBN 13 : 9401153388
Total Pages : 622 pages
Book Rating : 4.4/5 (11 download)
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.
Author : Ming-Jun Lai
Publisher : Cambridge University Press
ISBN 13 : 0521875927
Total Pages : 28 pages
Book Rating : 4.5/5 (218 download)
Download or read book Spline Functions on Triangulations written by Ming-Jun Lai and published by Cambridge University Press. This book was released on 2007-04-19 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive graduate text offering a detailed mathematical treatment of polynomial splines on triangulations.
Author : R. Arcangéli
Publisher : Springer Science & Business Media
ISBN 13 : 1402077866
Total Pages : 267 pages
Book Rating : 4.4/5 (2 download)
Download or read book Multidimensional Minimizing Splines written by R. Arcangéli and published by Springer Science & Business Media. This book was released on 2004-06-24 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is of interest to mathematicians, geologists, engineers and, in general, researchers and post graduate students involved in spline function theory, surface fitting problems or variational methods. From reviews: The book is well organized, and the English is very good. I recommend the book to researchers in approximation theory, and to anyone interested in bivariate data fitting." (L.L. Schumaker, Mathematical Reviews, 2005).
Author : S.P. Singh
Publisher : Springer Science & Business Media
ISBN 13 : 9401126348
Total Pages : 482 pages
Book Rating : 4.4/5 (11 download)
Download or read book Approximation Theory, Spline Functions and Applications written by S.P. Singh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the Proceedings of the NATO Advanced Study Institute on Approximation Theory, Spline Functions and Applications held in the Hotel villa del Mare, Maratea, Italy between April 28,1991 and May 9, 1991. The principal aim of the Advanced Study Institute, as reflected in these Proceedings, was to bring together recent and up-to-date developments of the subject, and to give directions for future research. Amongst the main topics covered during this Advanced Study Institute is the subject of uni variate and multivariate wavelet decomposition over spline spaces. This is a relatively new area in approximation theory and an increasingly impor tant subject. The work involves key techniques in approximation theory cardinal splines, B-splines, Euler-Frobenius polynomials, spline spaces with non-uniform knot sequences. A number of scientific applications are also highlighted, most notably applications to signal processing and digital im age processing. Developments in the area of approximation of functions examined in the course of our discussions include approximation of periodic phenomena over irregular node distributions, scattered data interpolation, Pade approximants in one and several variables, approximation properties of weighted Chebyshev polynomials, minimax approximations, and the Strang Fix conditions and their relation to radial functions. I express my sincere thanks to the members of the Advisory Commit tee, Professors B. Beauzamy, E. W. Cheney, J. Meinguet, D. Roux, and G. M. Phillips. My sincere appreciation and thanks go to A. Carbone, E. DePas cale, R. Charron, and B.
Author : Larry L. Schumaker
Publisher : SIAM
ISBN 13 : 1611973899
Total Pages : 420 pages
Book Rating : 4.6/5 (119 download)
Download or read book Spline Functions written by Larry L. Schumaker and published by SIAM. This book was released on 2015-08-13 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. ?
Author : Serge Dubuc
Publisher : American Mathematical Soc.
ISBN 13 : 0821808753
Total Pages : 409 pages
Book Rating : 4.8/5 (218 download)
Download or read book Spline Functions and the Theory of Wavelets written by Serge Dubuc and published by American Mathematical Soc.. This book was released on 1999 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : S.P. Singh
Publisher : Springer Science & Business Media
ISBN 13 : 9400964668
Total Pages : 481 pages
Book Rating : 4.4/5 (9 download)
Download or read book Approximation Theory and Spline Functions written by S.P. Singh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: A NATO Advanced Study Institute on Approximation Theory and Spline Functions was held at Memorial University of Newfoundland during August 22-September 2, 1983. This volume consists of the Proceedings of that Institute. These Proceedings include the main invited talks and contributed papers given during the Institute. The aim of these lectures was to bring together Mathematicians, Physicists and Engineers working in the field. The lectures covered a wide range including ~1ultivariate Approximation, Spline Functions, Rational Approximation, Applications of Elliptic Integrals and Functions in the Theory of Approximation, and Pade Approximation. We express our sincere thanks to Professors E. W. Cheney, J. Meinguet, J. M. Phillips and H. Werner, members of the International Advisory Committee. We also extend our thanks to the main speakers and the invi ted speakers, whose contri butions made these Proceedings complete. The Advanced Study Institute was financed by the NATO Scientific Affairs Division. We express our thanks for the generous support. We wish to thank members of the Department of Mathematics and Statistics at MeMorial University who willingly helped with the planning and organizing of the Institute. Special thanks go to Mrs. Mary Pike who helped immensely in the planning and organizing of the Institute, and to Miss Rosalind Genge for her careful and excellent typing of the manuscript of these Proceedings.
Author : Klaus Hollig
Publisher : SIAM
ISBN 13 : 1611972949
Total Pages : 228 pages
Book Rating : 4.6/5 (119 download)
Download or read book Approximation and Modeling with B-Splines written by Klaus Hollig and published by SIAM. This book was released on 2015-07-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Larry L. Schumaker
Publisher :
ISBN 13 : 9781107173774
Total Pages : 582 pages
Book Rating : 4.1/5 (737 download)
Download or read book Spline Functions written by Larry L. Schumaker and published by . This book was released on 2007 with total page 582 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.
Author : Carl de Boor
Publisher : Springer
ISBN 13 : 0387953663
Total Pages : 348 pages
Book Rating : 4.3/5 (879 download)
Download or read book A Practical Guide to Splines written by Carl de Boor and published by Springer. This book was released on 2001-12-01 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the author’s experience with calculations involving polynomial splines, presenting those parts of the theory especially useful in calculations and stressing the representation of splines as weighted sums of B-splines. The B-spline theory is developed directly from the recurrence relations without recourse to divided differences. This reprint includes redrawn figures, and most formal statements are accompanied by proofs.
Author : Paul Leo Butzer
Publisher :
ISBN 13 :
Total Pages : 286 pages
Book Rating : 4.:/5 (89 download)
Download or read book On Approximation Theory written by Paul Leo Butzer and published by . This book was released on 1964 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Charles K. Chui
Publisher : SIAM
ISBN 13 : 0898712262
Total Pages : 192 pages
Book Rating : 4.8/5 (987 download)
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.
Author : Samuel Karlin
Publisher :
ISBN 13 :
Total Pages : 520 pages
Book Rating : 4.3/5 (91 download)
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.
