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

“The author can only be congratulated for this work which will provide useful material for readers for years to come.”