Variational Theory Of Splines
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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.
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.
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.
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 And The Theory Of Wavelets
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Author : Serge Dubuc
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
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 with Spline theory 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.
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.
An Identity For Spline Functions With Applications To Variation Diminishing Spline Approximation
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Author : Martin J. Marsden
language : en
Publisher:
Release Date : 1968
An Identity For Spline Functions With Applications To Variation Diminishing Spline Approximation written by Martin J. Marsden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Convergence categories.
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).
Variational Views In Mechanics
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Author : Paolo Maria Mariano
language : en
Publisher: Springer Nature
Release Date : 2022-02-08
Variational Views In Mechanics written by Paolo Maria Mariano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-08 with Mathematics categories.
This volume provides a timely survey of interactions between the calculus of variations and theoretical and applied mechanics. Chapters have been significantly expanded since preliminary versions appeared in a special issue of the Journal of Optimization Theory and Applications (184(1), 2020) on “Calculus of Variations in Mechanics and Related Fields”. The variety of topics covered offers researchers an overview of problems in mechanics that can be analyzed with variational techniques, making this a valuable reference for researchers in the field. It also presents ideas for possible future areas of research, showing how the mastery of these foundational mathematical techniques can be used for many exciting applications. Specific topics covered include: Topology optimization Identification of material properties Optimal control Plastic flows Gradient polyconvexity Obstacle problems Quasi-monotonicity Variational Views in Mechanics will appeal to researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering.
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.