Meshfree Approximation Methods With Matlab (With Cd-rom)

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World Scientific Publishing Company, 2007 M04 17 - 520 páginas
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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.
 

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Contenido

1 Introduction
1
2 Radial Basis Function Interpolation in MATLAB
17
3 Positive Definite Functions
27
4 Examples of Strictly Positive Definite Radial Functions
37
5 Completely Monotone and Multiply Monotone Functions
47
6 Scattered Data Interpolation with Polynomial Precision
53
7 Conditionally Positive Definite Functions
63
8 Examples of Conditionally Positive Definite Functions
67
27 Numerical Experiments for Approximate MLS Approximation
237
28 Fast Fourier Transforms
243
29 Partition of Unity Methods
249
30 Approximation of Point Cloud Data in 3D
255
31 Fixed Level Residual Iteration
265
32 Multilevel Iteration
277
33 Adaptive Iteration
291
34 Improving the Condition Number of the Interpolation Matrix
303

9 Conditionally Positive Definite Radial Functions
73
Other Norms and Scattered Data Fitting on Manifolds
79
11 Compactly Supported Radial Basis Functions
85
12 Interpolation with Compactly Supported RBFs in MATLAB
95
13 Reproducing Kernel Hilbert Spaces and Native Spaces for Strictly Positive Definite Functions
103
14 The Power Function and Native Space Error Estimates
111
15 Refined and Improved Error Bounds
125
16 Stability and Tradeoff Principles
135
17 Numerical Evidence for Approximation Order Results
141
18 The Optimality of RBF Interpolation
159
19 Least Squares RBF Approximation with MATLAB
165
20 Theory for Least Squares Approximation
177
21 Adaptive Least Squares Approximation
181
22 Moving Least Squares Approximation
191
23 Examples of MLS Generating Functions
205
24 MLS Approximation with MATLAB
211
25 Error Bounds for Moving Least Squares Approximation
225
26 Approximate Moving Least Squares Approximation
229
35 Other Efficient Numerical Methods
321
36 Generalized Hermite Interpolation
333
37 RBF Hermite Interpolation in MATLAB
339
38 Solving Elliptic Partial Differential Equations via RBF Collocation
345
39 NonSymmetric RBF Collocation in MATLAB
353
40 Symmetric RBF Collocation in MATLAB
365
41 Collocation with CSRBFs in MATLAB
375
42 Using Radial Basis Functions in Pseudospectral Mode
387
43 RBFPS Methods in MATLAB
401
44 RBF Galerkin Methods
419
45 RBF Galerkin Methods in MATLAB
423
Appendix A Useful Facts from Discrete Mathematics
427
Appendix B Useful Facts from Analysis
431
Appendix C Additional Computer Programs
435
Appendix D Catalog of RBFs with Derivatives
443
Bibliography
451
Index
491
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Acerca del autor (2007)

Gregory E Fasshauer (Illinois Institute of Technology, USA)

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