Meshfree Approximation Methods with Matlab

Gregory E. Fasshauer - Collection Interdisciplinary Mathematical Sciences

500 pages, parution le 30/05/2007

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Résumé

Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. Meshfree approximation methods, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view. A good balance is supplied between the necessary theory and implementation in terms of many MATLAB programs, with examples and applications to illustrate key points. Used as class notes for graduate courses at Northwestern University, Illinois Institute of Technology, and Vanderbilt University, this book will appeal to both mathematics and engineering graduate students.

Sommaire

Introduction
Radial basis function interpolation in MATLAB
Positive definite functions
Examples of strictly positive definite radial functions
Completely monotone and multiply monotone functions
Scattered data interpolation with polynomial precision
Conditionally positive definite functions
Examples of conditionally positive definite functions
Conditionally positive definite radial functions
Miscellaneous theory: other norms and scattered data fitting on manifolds
Compactly supported radial basis functions
Interpolation with compactly supported RBFs in MATLAB
Reproducing Kernel Hilbert spaces and native spaces for strictly positive definite functions
The power function and native space error estimates
Refined and improved error bounds
Stability and trade-off principles
Numerical evidence for approximation order results
The optimally of RBF interpolation
Least squares RBF approximation with MATLAB
Theory for least squares approximation
Adaptive least squares approximation
Moving least squares approximation
Examples of MLS generating functions
MLS approximation with MATLAB

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Caractéristiques techniques

	PAPIER
Éditeur(s)	World Scientific Publishing Company
Auteur(s)	Gregory E. Fasshauer
Collection	Interdisciplinary Mathematical Sciences
Parution	30/05/2007
Nb. de pages	500
Couverture	Broché
Intérieur	Noir et Blanc
EAN13	9789812706331
ISBN13	978-9-81270-633-1