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Author : Ming-Jun Lai,Larry L. Schumaker
Publisher : Cambridge University Press
Page : 28 pages
File Size : 47,7 Mb
Release : 2007-04-19
Category : Mathematics
ISBN : 9780521875929
Comprehensive graduate text offering a detailed mathematical treatment of polynomial splines on triangulations.
Author : Larry L. Schumaker
Publisher : SIAM
Page : 413 pages
File Size : 41,8 Mb
Release : 2015-01-01
Category : Science
ISBN : 9781611973907
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 : Ren-Hong Wang
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 49,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401723787
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.
Author : Gregory E. Fasshauer,Larry L. Schumaker
Publisher : Springer
Page : 398 pages
File Size : 49,6 Mb
Release : 2017-07-19
Category : Mathematics
ISBN : 9783319599120
These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, approximation of fractional differential equations, numerical integration formulas, and trigonometric polynomial approximation.
Author : Charles K. Chui
Publisher : SIAM
Page : 192 pages
File Size : 52,8 Mb
Release : 1988-01-01
Category : Mathematics
ISBN : 9780898712261
Subject of multivariate splines presented from an elementary point of view; includes many open problems.
Author : Gregory E. Fasshauer,Marian Neamtu,Larry L. Schumaker
Publisher : Springer Nature
Page : 256 pages
File Size : 46,9 Mb
Release : 2021-01-04
Category : Mathematics
ISBN : 9783030574642
These proceedings are based on the international conference Approximation Theory XVI held on May 19–22, 2019 in Nashville, Tennessee. The conference was the sixteenth in a series of meetings in Approximation Theory held at various locations in the United States. Over 130 mathematicians from 20 countries attended. The book contains two longer survey papers on nonstationary subdivision and Prony’s method, along with 11 research papers on a variety of topics in approximation theory, including Balian-Low theorems, butterfly spline interpolation, cubature rules, Hankel and Toeplitz matrices, phase retrieval, positive definite kernels, quasi-interpolation operators, stochastic collocation, the gradient conjecture, time-variant systems, and trivariate finite elements. The book should be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Author : Larry Schumaker
Publisher : Cambridge University Press
Page : 524 pages
File Size : 43,7 Mb
Release : 2007-08-16
Category : Mathematics
ISBN : 9781139463430
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 : Serge Dubuc,Gilles Deslauriers
Publisher : American Mathematical Soc.
Page : 412 pages
File Size : 44,7 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 0821870181
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 : George Anastassiou
Publisher : CRC Press
Page : 413 pages
File Size : 52,7 Mb
Release : 2019-06-03
Category : Mathematics
ISBN : 9780429525117
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 : Charles K Chui,Larry L Schumaker
Publisher : World Scientific
Page : 606 pages
File Size : 46,8 Mb
Release : 1995-11-07
Category : Mathematics
ISBN : 9789814549066
This is the collection of the refereed and edited papers presented at the 8th Texas International Conference on Approximation Theory. It is interdisciplinary in nature and consists of two volumes. The central theme of Vol. I is the core of approximation theory. It includes such important areas as qualitative approximations, interpolation theory, rational approximations, radial-basis functions, and splines. The second volume focuses on topics related to wavelet analysis, including multiresolution and multi-level approximation, subdivision schemes in CAGD, and applications.
Author : Charles K. Chui
Publisher : World Scientific
Page : 606 pages
File Size : 45,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9789814532594
This is the collection of the refereed and edited papers presented at the 8th Texas International Conference on Approximation Theory. It is interdisciplinary in nature and consists of two volumes. The central theme of Vol. I is the core of approximation theory. It includes such important areas as qualitative approximations, interpolation theory, rational approximations, radial-basis functions, and splines. The second volume focuses on topics related to wavelet analysis, including multiresolution and multi-level approximation, subdivision schemes in CAGD, and applications.
Author : K. Bohmer,G. Meinardus,W. Schempp
Publisher : Unknown
Page : 436 pages
File Size : 55,6 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 3662200139
Author : Hartmut Prautzsch,Wolfgang Boehm,Marco Paluszny
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 45,5 Mb
Release : 2013-04-17
Category : Computers
ISBN : 9783662049198
This book provides a solid and uniform derivation of the various properties Bezier and B-spline representations have, and shows the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer Aided Geometric Design and provides a clear and illustrative presentation of the basic principles, as well as a treatment of advanced material including multivariate splines, some subdivision techniques and constructions of free form surfaces with arbitrary smoothness. The text is beautifully illustrated with many excellent figures to emphasize the geometric constructive approach of this book.
Author : D. Bainov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 476 pages
File Size : 49,9 Mb
Release : 2020-05-18
Category : Mathematics
ISBN : 9783112313923
No detailed description available for "Proceedings of the Eighth International Colloquium on Differential Equations, Plovdiv, Bulgaria, 18-23 August, 1997".
Author : Gheorghe Micula,Sanda Micula
Publisher : Springer Science & Business Media
Page : 622 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401153386
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.