Topics In Multivariate Approximation And Interpolation
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Topics In Multivariate Approximation And Interpolation
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Author : Kurt Jetter
language : en
Publisher: Elsevier
Release Date : 2005-11-15
Topics In Multivariate Approximation And Interpolation written by Kurt Jetter and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-15 with Mathematics categories.
This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for graduate students specializing in these topics, and for researchers in universities and in industry. - A collection of articles of highest scientific standard - An excellent introduction and overview of recent topics from multivariate approximation - A valuable source of references for specialists in the field - A representation of the state-of-the-art in selected areas of multivariate approximation - A rigorous mathematical introduction to special topics of interdisciplinary research
Topics In Multivariate Approximation
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Author : C. K. Chui
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Topics In Multivariate Approximation written by C. K. Chui and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Topics in Multivariate Approximation contains the proceedings of an international workshop on multivariate approximation held at the University of Chile in Santiago, Chile, on December 15-19, 1986. Leading researchers in the field discussed several problem areas related to multivariate approximation and tackled topics ranging from multivariate splines and fitting of scattered data to tensor approximation methods and multivariate polynomial approximation. Numerical grid generation and finite element methods were also explored, along with constrained interpolation and smoothing. Comprised of 22 chapters, this book first describes the application of Boolean methods of approximation in combination with the theory of right invertible operators to bivariate Fourier expansions. The reader is then introduced to ill-posed problems in multivariate approximation; interpolation of scattered data by radial functions; and shape-preserving surface interpolation. Subsequent chapters focus on approximation by harmonic functions; numerical generation of nested series of general triangular grids; triangulation methods; and inequalities arising from best local approximations in rectangles. A bibliography of multivariate approximation concludes the book. This monograph will be of interest to mathematicians.
Advanced Topics In Multivariate Approximation Proceedings Of The International Workshop
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Author : F Fontanella
language : en
Publisher: World Scientific
Release Date : 1996-11-13
Advanced Topics In Multivariate Approximation Proceedings Of The International Workshop written by F Fontanella and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-13 with categories.
This volume consists of 24 refereed carefully edited papers on various topics in multivariate approximation. It represents the proceedings of a workshop organized by the University of Firenze, and held in September 1995 in Montecatini, Italy.The main themes of the volume are multiresolution analysis and wavelets, multidimensional interpolation and smoothing, and computer-aided geometric design. A number of particular topics are included, like subdivision algorithms, constrained approximation and shape-preserving algorithms, thin plate splines, radial basis functions, treatment of scattered data, rational surfaces and offsets, blossoming, grid generation, surface reconstruction, algebraic curves and surfaces, and neural networks.
Interpolation And Approximation By Polynomials
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Author : George M. Phillips
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-04-08
Interpolation And Approximation By Polynomials written by George M. Phillips 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 2003-04-08 with Mathematics categories.
In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. The author is well known for his clarity of writing and his many contributions as a researcher in approximation theory.
Multivariate Splines
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Author : Charles K. Chui
language : en
Publisher: SIAM
Release Date : 1988-01-01
Multivariate Splines written by Charles K. Chui and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
Subject of multivariate splines presented from an elementary point of view; includes many open problems.
Spline Functions And Multivariate Interpolations
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Author : Borislav D. Bojanov
language : en
Publisher: Springer
Release Date : 1993-03-31
Spline Functions And Multivariate Interpolations written by Borislav D. Bojanov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-03-31 with Computers categories.
This volume provides a comprehensive introduction to the theory of spline functions. Emphasis is given to new developments, such as the general Birkhoff-type interpolation, the extremal properties of splines, their prominent role in the optimal recovery of functions, and multivariate interpolation by polynomials and splines. The book has thirteen chapters dealing, respectively, with interpolation by algebraic polynomials, the space of splines, B-splines, interpolation by spline functions, natural spline functions, perfect splines, monosplines, periodic splines, multivariate B-splines and truncated powers, multivariate spline functions and divided differences, box splines, multivariate mean value interpolation, multivariate polynomial interpolations arising by hyperplanes, and multivariate pointwise interpolation. Some of the results described are presented as exercises and hints are given for their solution. For researchers and graduate students whose work involves approximation theory.
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.
Multivariate Polynomial Approximation
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Author : Manfred Reimer
language : en
Publisher: Springer Science & Business Media
Release Date : 2003
Multivariate Polynomial Approximation written by Manfred Reimer 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 2003 with Mathematics categories.
Multivariate polynomials are a main tool in approximation. The book begins with an introduction to the general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators. On this background, the book gives the first comprehensive introduction to the recently developped theory of generalized hyperinterpolation. As an application, the book gives a quick introduction to tomography. Several parts of the book are based on rotation principles, which are presented in the beginning of the book, together with all other basic facts needed.
Multivariate Approximation From Cagd To Wavelets Proceedings Of The International Workshop
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Author : Kurt Jetter
language : en
Publisher: World Scientific
Release Date : 1993-11-30
Multivariate Approximation From Cagd To Wavelets Proceedings Of The International Workshop written by Kurt Jetter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-11-30 with categories.
Contents: Fast Algorithms for Simultaneous Polynomial Approximation (G Baszenski & M Tasche)α-Spline of Smoothing for Correlated Errors in Dimension Two (M Bozzini & L Lenarduzzi)New Developments in the Theory of Radial Basis Function Interpolation (M D Buhmann)Realization of Neural Networks with One Hidden Layer (C K Chui & X Li)A General Method for Constrained Curves with Boundary Conditions (P Costantini)Sign-Regular and Totally Positive Matrices: An Algorithmic Approach (M Gasca & J M Peña)Some Results on Blossoming and Multivariate B-Splines (R Gormaz & P-J Laurent)Riesz Bounds in Scattered Data Interpolation and L2-Approximation (K Jetter)On Multivariate Hermite Polynomial Interpolation (A Le Méhauté)Quantitative Approximation Results for Sigma-Pi-Type Neural Network Operators (B Lenze)Local Interpolation Schemes — From Curves to Surfaces (D Levin)Some Results on Approximation by Smoothing Dm-Splines (M C L de Silanes) Readership: Applied mathematicians.
Approximation Theory Wavelets And Applications
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Author : S.P. Singh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Approximation Theory Wavelets 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 2013-03-09 with Mathematics categories.
Approximation Theory, Wavelets and Applications draws together the latest developments in the subject, provides directions for future research, and paves the way for collaborative research. The main topics covered include constructive multivariate approximation, theory of splines, spline wavelets, polynomial and trigonometric wavelets, interpolation theory, polynomial and rational approximation. Among the scientific applications were de-noising using wavelets, including the de-noising of speech and images, and signal and digital image processing. In the area of the approximation of functions the main topics include multivariate interpolation, quasi-interpolation, polynomial approximation with weights, knot removal for scattered data, convergence theorems in Padé theory, Lyapunov theory in approximation, Neville elimination as applied to shape preserving presentation of curves, interpolating positive linear operators, interpolation from a convex subset of Hilbert space, and interpolation on the triangle and simplex. Wavelet theory is growing extremely rapidly and has applications which will interest readers in the physical, medical, engineering and social sciences.