Spline Functions
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Spline Functions And Multivariate Interpolations
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Author : Borislav D. Bojanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Spline Functions And Multivariate Interpolations written by Borislav D. Bojanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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 Basic Theory
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Author : Larry Schumaker
language : en
Publisher: Cambridge University Press
Release Date : 2007-08-16
Spline Functions Basic Theory written by Larry Schumaker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-16 with Mathematics categories.
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.
Spline Functions On Triangulations
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Author : Ming-Jun Lai
language : en
Publisher: Cambridge University Press
Release Date : 2007-04-19
Spline Functions On Triangulations written by Ming-Jun Lai and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-19 with Mathematics categories.
Comprehensive graduate text offering a detailed mathematical treatment of polynomial splines on triangulations.
Spline Functions
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Author : Larry L. Schumaker
language : en
Publisher: SIAM
Release Date : 2024-12-09
Spline Functions written by Larry L. Schumaker and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-09 with Mathematics categories.
This book is a continuation of the author’s earlier book Spline Functions: Computational Methods, published in 2015 by SIAM. This new book focuses on computational methods developed in the last ten years that make use of splines to approximate functions and data and to solve boundary-value problems. The first half of the book works with bivariate spaces of splines defined on H-triangulations, T-meshes, and curved triangulations. Trivariate tensor-product splines and splines on tetrahedral partitions are also discussed. The second half of the book makes use of these spaces to solve boundary-value problems, with a special emphasis on elliptic PDEs defined on curved domains. The book contains numerous examples and figures to illustrate the methods and their performance. In addition to the included bibliography, a 125-page list of additional references can be downloaded from the SIAM website. All of the algorithms in the book have been coded in MATLAB and are included in a package that can also be downloaded from the website. It can be used to run all of the examples in the book. The package also provides an extensive toolbox of functions that readers can utilize to develop their own spline software. The book is designed for mathematicians, engineers, scientists, and anyone else wanting to make use of spline functions for numerical computation.
Spline Functions
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Author : K. Böhmer
language : en
Publisher: Springer
Release Date : 2006-11-14
Spline Functions written by K. Böhmer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Approximation Theory Spline Functions And Applications
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Author : S.P. Singh
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Approximation Theory Spline Functions And Applications written by S.P. Singh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Multivariate Spline Functions And Their Applications
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Author : Ren-Hong Wang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Multivariate Spline Functions And Their Applications written by Ren-Hong Wang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book deals with the algebraic geometric method of studying multivariate splines. Topics treated include: the theory of multivariate spline spaces, higher-dimensional splines, rational splines, piecewise algebraic variety (including piecewise algebraic curves and surfaces) and applications in the finite element method and computer-aided geometric design. Many new results are given. Audience: This volume will be of interest to researchers and graduate students whose work involves approximations and expansions, numerical analysis, computational geometry, image processing and CAD/CAM.
Numerical Differentiation By Spline Functions And Its Application To Analyzing A Lake Temperature Observation
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Author : Shunsuke Takagi
language : en
Publisher:
Release Date : 1971
Numerical Differentiation By Spline Functions And Its Application To Analyzing A Lake Temperature Observation written by Shunsuke Takagi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Heat categories.
Numerical differentiation by use of classical interpolation formulas yields a diversity of results. Consistent numerical differentiation can be performed by using a spline function as an interpolating function. As an application, temperature observed in a lake is numerically differentiated as a function of time and of depth by use of cubic splines. The deviation of the actual heat transfer mechanism from vertical heat conduction can thus be detected. The reliability of numerical differentiation by spline functions is manifest in this example. (Author).
Spline Functions And The Theory Of Wavelets
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Author : Serge Dubuc
language : en
Publisher: American Mathematical Soc.
Release Date : 1999-01-01
Spline Functions And The Theory Of Wavelets written by Serge Dubuc and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Mathematics categories.
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.
Handbook On Splines For The User
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Author : Eugene V. Shikin
language : en
Publisher: CRC Press
Release Date : 1995-07-14
Handbook On Splines For The User written by Eugene V. Shikin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-14 with Mathematics categories.
Splines find ever increasing application in the numerical methods, computer-aided design, and computer graphics areas. The Handbook on Splines for the User not only provides an excellent introduction to basic concepts and methods but also includes the SplineGuide-a computer diskette that allows the reader to practice using important programs.These programs help the user to build interpolating and smoothing cubic and bicubic splines of all classes. Programs are described in Fortran for spline functions and C for geometric splines. The Handbook describes spline functions and geometric splines and provides simple, but effective algorithms. It covers virtually all of the important types of cubic and bicubic splines, functions, variables, curves, and surfaces. The book is written in a straightforward manner and requires little mathematical background. When necessary, the authors give theoretical treatments in an easy-to-use form. Through the Handbook on Splines for the User, introduce yourself to the exciting world of splines and learn to use them in practical applications and computer graphics.