Meshfree approximation methods with Matlab [electronic resource] / Gregory E. Fasshauer.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Title from web page (viewed November 20, 2018).

Includes bibliographical references (p. 451-489) and index.

Introduction -- Radial basis function interpolation in MATLAB -- Positive definite functions -- Examples of strictly positive definite radial functions -- Completely monotone and multiply monotone functions -- Scattered data interpolation with polynomial precision -- Conditionally positive definite functions -- Examples of conditionally positive definite functions -- Conditionally positive definite radial functions -- Miscellaneous theory: Other norms and scattered data fitting on manifolds -- Compactly supported radial basis functions -- Interpolation with compactly supported RBFs in MATLAB -- Reproducing kernel Hilbert spaces and native spaces for strictly positive definite functions -- The power function and native space error estimates -- Refined and improved error bounds -- Stability and trade-off principles -- Numerical evidence for approximation order results -- The optimality of RBF interpolation -- Least squares RBF approximation with MATLAB -- Theory for least squares approximation -- Adaptive least squares approximation -- Moving least squares approximation -- Examples of MLS generating functions -- MLS approximation with MATLAB -- Error bounds for moving least squares approximation -- Approximate moving least squares approximation -- Numerical experiments for approximate MLS approximation -- Fast fourier transforms -- Partition of unity methods -- Approximation of point cloud data in 3D -- Fixed level residual iteration -- Multilevel iteration -- Adaptive iteration -- Improving the condition number of the interpolation matrix -- Other efficient numerical methods -- Generalized Hermite interpolation -- RBF Hermite interpolation in MATLAB -- Solving elliptic partial differential equations via RBF collocation -- Non-symmetric RBF collocation in MATLAB -- Symmetric RBF collocation in MATLAB -- Collocation with CSRBFs in MATLAB -- Using radial basis functions in pseudospectral mode -- RBF-PS methods in MATLAB -- RBF Galerkin methods -- RBF Galerkin methods in MATLAB.

"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."--Publisher's website.