# Meshfree Approximation Methods With Matlab (With Cd-rom)

World Scientific Publishing Company, 2007 M04 17 - 520 páginas
0 Opiniones
Las opiniones no están verificadas, pero Google revisa que no haya contenido falso y lo quita si lo identifica
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.

### Comentarios de la gente -Escribir un comentario

No encontramos ningún comentario en los lugares habituales.

### 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 Derechos de autor

### Acerca del autor (2007)

Gregory E Fasshauer (Illinois Institute of Technology, USA)