Description
Book SynopsisMeshfree 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.
Table of ContentsCompletely and Multiply Monotone Functions; Scattered Data Interpolation with Polynomial Precision; Miscellaneous Theory: Other Norms and Scattered Data Fitting on Manifolds; Compactly Supported Radial Basis Functions; The Optimality of RBF Interpolation; Theory for Least Squares Approximation; Moving Least Squares Approximation; Approximation of Point Cloud Data in 3D; Adaptive Iteration; Generalized Hermite Interpolation; RBF Galerkin Methods; and other papers.
