Splines And Variational Methods
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Splines And Variational Methods
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Author : P. M. Prenter
language : en
Publisher: Courier Corporation
Release Date : 2013-11-26
Splines And Variational Methods written by P. M. Prenter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-26 with Mathematics categories.
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.
Variational Theory Of Splines
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Author : Anatoly Yu. Bezhaev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Variational Theory Of Splines written by Anatoly Yu. Bezhaev 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 2013-04-18 with Mathematics categories.
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.
Multidimensional Minimizing Splines
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Author : R. Arcangéli
language : en
Publisher: Springer
Release Date : 2013-05-08
Multidimensional Minimizing Splines written by R. Arcangéli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-08 with Mathematics categories.
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).
Variational Regularization Of 3d Data
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Author : Hebert Montegranario
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-03-14
Variational Regularization Of 3d Data written by Hebert Montegranario 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 2014-03-14 with Computers categories.
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.
Variational Methods In Imaging
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Author : Otmar Scherzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-26
Variational Methods In Imaging written by Otmar Scherzer 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 2008-09-26 with Mathematics categories.
This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Many numerical examples accompany the theory throughout the text. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.
Finite Element Methods With B Splines
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Author : Klaus Hollig
language : en
Publisher: SIAM
Release Date : 2012-12-13
Finite Element Methods With B Splines written by Klaus Hollig and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-13 with Mathematics categories.
An exploration of the new weighted approximation techniques which result from the combination of the finite element method and B-splines.
Multivariate Polysplines
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Author : Ognyan Kounchev
language : en
Publisher: Academic Press
Release Date : 2001-06-11
Multivariate Polysplines written by Ognyan Kounchev and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-11 with Mathematics categories.
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
Spline Functions
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Author : Larry L. Schumaker
language : en
Publisher: SIAM
Release Date : 2015-01-01
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 2015-01-01 with Science categories.
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.
Multivariate Approximation And Splines
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Author : Günther Nürnberger
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Multivariate Approximation And Splines written by Günther Nürnberger and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Topics In Splines And Applications
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Author : Young Kinh-Nhue Truong
language : en
Publisher: BoD – Books on Demand
Release Date : 2018-06-06
Topics In Splines And Applications written by Young Kinh-Nhue Truong and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-06 with Computers categories.
Splines provide a significant tool for the design of computationally economical curves and surfaces for the construction of various objects like automobiles, ship hulls, airplane fuselages and wings, propeller blades, shoe insoles, bottles, etc. It also contributes in the description of geological, physical, statistical, and even medical phenomena. Spline methods have proven to be indispensable in a variety of modern industries, including computer vision, robotics, signal and image processing, visualization, textile, graphic designs, and even media. This book aims to provide a valuable source on splines and their applications. It focuses on collecting and disseminating information in various disciplines including computer-aided geometric design, computer graphics, data visualization, data fitting, power systems, clinical and epidemiologic studies, disease detection, regression curves, social media, and biological studies. The book is useful for researchers, scientists, practitioners, and many others who seek state-of-the-art techniques and applications using splines. It is also useful for undergraduate senior students as well as graduate students in the areas of computer science, engineering, health science, statistics, and mathematics. Each chapter also provides useful information on software developments and their extensions.