Meshfree Approximation Methods with MATLAB
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 result 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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Surface Fitting and Multiresolution Methods, Volume 2
Alain Le Méhauté,Christophe Rabut,Larry L. Schumaker
No preview available - 1997
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
Conditionally Positive Definite Radial Functions
Numerical Experiments for Approximate MLS Approximation
Fast Fourier Transforms
Partition of Unity Methods
Approximation of Point Cloud Data in 3D
Fixed Level Residual Iteration
Improving the Condition Number of the Interpolation Matrix
Other Norms and Scattered Data Fitting
Compactly Supported Radial Basis Functions
Interpolation with Compactly Supported RBFs in Matlab
Reproducing Kernel Hilbert Spaces and Native Spaces
The Power Function and Native Space Error Estimates
Refined and Improved Error Bounds
Stability and TradeOff Principles
Numerical Evidence for Approximation Order Results
The Optimality of RBF Interpolation
Least Squares RBF Approximation with Matlab
Theory for Least Squares Approximation
Moving Least Squares Approximation
Examples of MLS Generating Functions
MLS Approximation with Matlab
Error Bounds for Moving Least Squares Approximation
Other Efficient Numerical Methods
Generalized Hermite Interpolation
RBF Hermite Interpolation in Matlab
Solving Elliptic Partial Differential Equations via RBF Collocation
NonSymmetric RBF Collocation in Matlab
Symmetric RBF Collocation in MATLAB
Collocation with CSRBFs in Matlab
Using Radial Basis Functions in Pseudospectral Mode
RBFPS Methods in Matlab
RBF Galerkin Methods
Appendix A Useful Facts from Discrete Mathematics
Additional Computer Programs
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MESHFREE APPROXIMATION METHODS WITH MATLAB
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