Review of A Course in Approximation Theory by Ward Cheney and Will Light PDF appeared in Mathematical Monthly May 2004, 448-452.
Over the past several years meshfree approximation methods have found their way. These methods come in various flavors, most of which can be explained either by what is known in the literature as radial basis functions (RBFs), or in terms of the moving least squares (MLS) method.
Schommers (eds.), American Scientific Publishers, 2006, 33-97. Meshfree methods are the topic of recent research in many areas of computational science and approximation theory. 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. Meshfree Methods PDF to appear in Handbook of Theoretical and Computational Nanotechnology, M. 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. Function (RBF) methods are such meshfree techniques which are very popular due to their meshless nature and ease of implementation. Schreiner and Franke 1997, Freeden, Gervens and Schreiner 1998, Fasshauer. 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. recent applications in areas like machine learning and meshless methods for. Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present.
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