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Variational Theory Of Splines
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Book Synopsis Variational Theory of Splines by : Anatoly Yu. Bezhaev
Download or read book Variational Theory of Splines written by Anatoly Yu. Bezhaev and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a systematic description of the variational theory of splines in Hilbert spaces. All central aspects are discussed in the general form: existence, uniqueness, characterization via reproducing mappings and kernels, convergence, error estimations, vector and tensor hybrids in splines, dimensional reducing (traces of splines onto manifolds), etc. All considerations are illustrated by practical examples. In every case the numerical algorithms for the construction of splines are demonstrated.
Book Synopsis Splines and Variational Methods by : P. M. Prenter
Download or read book Splines and Variational Methods written by P. M. Prenter and published by Courier Corporation. This book was released on 2013-11-26 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text’s first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimensions. Additional topics include least squares and other Galerkin methods. Many helpful definitions, examples, and exercises appear throughout the book. A classic reference in spline theory, this volume will benefit experts as well as students of engineering and mathematics.
Book Synopsis Multidimensional Minimizing Splines by : R. Arcangéli
Download or read book Multidimensional Minimizing Splines written by R. Arcangéli and published by Springer. This book was released on 2013-05-08 with total page 263 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).
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.
Book Synopsis Multidimensional Minimizing Splines by : R. Arcangéli
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).
Book Synopsis Spline Functions on Triangulations by : Ming-Jun Lai
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.
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 413 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.
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.
Book Synopsis Variational Regularization of 3D Data by : Hebert Montegranario
Download or read book Variational Regularization of 3D Data written by Hebert Montegranario and published by Springer Science & Business Media. This book was released on 2014-03-14 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational Regularization of 3D Data provides an introduction to variational methods for data modelling and its application in computer vision. In this book, the authors identify interpolation as an inverse problem that can be solved by Tikhonov regularization. The proposed solutions are generalizations of one-dimensional splines, applicable to n-dimensional data and the central idea is that these splines can be obtained by regularization theory using a trade-off between the fidelity of the data and smoothness properties. As a foundation, the authors present a comprehensive guide to the necessary fundamentals of functional analysis and variational calculus, as well as splines. The implementation and numerical experiments are illustrated using MATLAB®. The book also includes the necessary theoretical background for approximation methods and some details of the computer implementation of the algorithms. A working knowledge of multivariable calculus and basic vector and matrix methods should serve as an adequate prerequisite.
Book Synopsis Reproducing Kernel Hilbert Spaces in Probability and Statistics by : Alain Berlinet
Download or read book Reproducing Kernel Hilbert Spaces in Probability and Statistics written by Alain Berlinet and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers theoretical questions including the latest extension of the formalism, and computational issues and focuses on some of the more fruitful and promising applications, including statistical signal processing, nonparametric curve estimation, random measures, limit theorems, learning theory and some applications at the fringe between Statistics and Approximation Theory. It is geared to graduate students in Statistics, Mathematics or Engineering, or to scientists with an equivalent level.
Book Synopsis Approximation and Modeling with B-Splines by : Klaus Hollig
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.
Book Synopsis An Identity for Spline Functions with Applications to Variation Diminishing Spline Approximation by : Martin J. Marsden
Download or read book An Identity for Spline Functions with Applications to Variation Diminishing Spline Approximation written by Martin J. Marsden and published by . This book was released on 1968 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: A spline function identity is developed and used to discuss the convergence properties of Schoenberg's variation diminishing spline approximation method. The Weierstrass approximation theorem is extended. Similar results for Chebshevian splines are developed. (Author).
Download or read book Spline Functions written by K. Böhmer and published by Springer. This book was released on 2006-11-14 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Element Methods with B-Splines by : Klaus Hollig
Download or read book Finite Element Methods with B-Splines written by Klaus Hollig and published by SIAM. This book was released on 2012-12-13 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of the new weighted approximation techniques which result from the combination of the finite element method and B-splines.
Book Synopsis Level Set Method in Medical Imaging Segmentation by : Ayman El-Baz
Download or read book Level Set Method in Medical Imaging Segmentation written by Ayman El-Baz and published by CRC Press. This book was released on 2019-06-26 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Level set methods are numerical techniques which offer remarkably powerful tools for understanding, analyzing, and computing interface motion in a host of settings. When used for medical imaging analysis and segmentation, the function assigns a label to each pixel or voxel and optimality is defined based on desired imaging properties. This often includes a detection step to extract specific objects via segmentation. This allows for the segmentation and analysis problem to be formulated and solved in a principled way based on well-established mathematical theories. Level set method is a great tool for modeling time varying medical images and enhancement of numerical computations.
Book Synopsis Multivariate Polysplines by : Ognyan Kounchev
Download or read book Multivariate Polysplines written by Ognyan Kounchev and published by Academic Press. This book was released on 2001-06-11 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Spline Functions and the Theory of Wavelets by : Serge Dubuc
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.
