Radial Basis Functions: Theory and Implementations: Preface

By M. Buhmann. 2003

2,026 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3a4daec37859e154f86d91619e77b4428dcd7fe3

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Citations in the corpus

• Limit problems for interpolation by analytic radial basis functions (2008, background): “There are now books of Buhmann [1] and Wendland [19] containing the background theory, and a recent survey [17] in Acta Numerica summarizes many applications.”
• False rumors detection on Sina Weibo by propagation structures (2015, background): “We extract a total of 23 features from each message propagation tree to build a vector for RBF kernel.”
• Numerical Cubature on Scattered Data by Radial Basis Functions (2005, methodology): “... the sampled function f :f orf sufficiently regular (technically, belonging to the “native space” of the given RBF) the bound α(h) may decrease exponentially (C ∞ RBF like G, MQ, IMQ), or algebraically (less smooth RBF like TPS, W2), as h → 0. We recall that another technical assumption is used i”
• The Golden Section Search Algorithm for Finding a Good Shape Parameter for Meshless Collocation Methods (2010, background): “In recent years radial basis functions (RBFs) [1] have emerged as an important tool in the development of meshless methods for solving partial differential equations (PDEs).”
• The Five Factor Model of personality and evaluation of drug consumption risk (2015, methodology): “We implemented the radial-basis functions method (Buhmann, 2003) for probability density function estimation (Scott, 1992).”
• Structural shape and topology optimization using a meshless Galerkin level set method (2012, background): “It is well-known that the RBFs with global support can ensure a higher accuracy of the interpolation but a fully dense matrix poorly conditioned [35], which restricts the practical applications of RBFs to a large set of scattered data.”