Many traditional numerical methods can either not handle such problems at all, or are limited to very special (regular) situations. Moreover, computation with high-dimensional data is an important issue in many areas of science and engineering. Thus, much of the work concerned with meshfree approximation methods is interdisciplinary - at the interface between mathematics and numerous application areas (see the partial list below). Meshfree methods have gained much attention in recent years, not only in the mathematics but also in the engineering community. Readership: Researchers and graduate students in the mathematics, science, and engineering fields who are interested in applications using multivariate meshfree approximation methods. Approximation of Point Cloud Data IN 3D.Approximate Moving Least Squares Approximation.Least Squares RBF Approximation with MATLAB.Reproducing Kernel Hilbert Spaces and Native Spaces for Strictly Positive Definite Functions.Compactly Supported Radial Basis Functions.Scattered Data Interpolation with Polynomial Precision.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. 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. 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. The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. 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. Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present.

Challenges in meshfree methods