Meshfree Approximation Methods with Matlab: (With CD-ROM) – PDF/EPUB Version Downloadable

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.
Contents:
Positive Definite Functions
Scattered Data Interpolation with Polynomial Precision
Compactly Supported Radial Basis Functions
Reproducing Kernel Hilbert Spaces and Native Spaces for Strictly Positive Definite Functions
Least Squares RBF Approximation with MATLAB
Moving Least Squares Approximation
Approximate Moving Least Squares Approximation
Partition of Unity Methods
Approximation of Point Cloud Data IN 3D
Fixed Level Residual Iteration
Generalized Hermite Interpolation
RBF Hermite Interpolation in MATLAB
RBF Galerkin Methods
and other topics

Readership: Researchers and graduate students in the mathematics, science, and engineering fields who are interested in applications using multivariate meshfree approximation methods.
Key Features:
Provides a balanced discussion of theory and implementation of meshfree approximation methods
Contains lots of MATLAB codes
Of interest to mathematicians as well as scientists and engineers