![]() ![]() 6 World Scientific Publishers, Singapore, 2007). Fasshauer, Meshfree Methods with Matlab (Interdisciplinary Mathematical Sciences, Vol. Wendland, Scattered Data Approximation (Cambridge University Press, 2005 (Hardback), 2010 (Paperback)). Solving PDEs with radial basis functions \end.Numerical aspects, multipole methods, partition of unity methods.Stability, analysis of the eigenvalues of the involved matrices.Error analysis, local polynomial reproduction, reflections on Sobolev spaces.Reproducing kernel Hilbert spaces, definition, properties, connection to positive definite functions.Compactly supported positive definite functions, dimension-dependent characterisations, dimension walk.Conditionally positive definite functions, polynomial reproduction.Positive definite functions, definition, properties, characterisations, examples.Interpolation in more than one space dimension.Radial basis functions are not only popular in the context of solving partial differential equations but also in computer graphics and learning theory. This course provides an introduction into the theory and numerics of radial basis functions, which form a major branch of meshfree methods. ![]() ![]() Compared to classical mesh-based methods like finite elements, finite volumes or finite differences, they provide more flexibility when it comes to problems with moving boundaries or to higher dimensional problems. Meshfree methods are a modern tool for the reconstruction of an unknown function, either directly or via solving a partial differential equation. ![]()
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