Green’s Functions: Taking Another Look at Kernel Approximation, Radial Basis Functions, and Splines

DOI10.1007/978-1-4614-0772-0_4zbMath1250.65107OpenAlexW87845680MaRDI QIDQ2912171

Gregory E. Fasshauer

Publication date: 14 September 2012

Published in: Springer Proceedings in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4614-0772-0_4

zbMATH Keywords

reproducing kernel Hilbert spacesradial basis functionseigenfunction expansionpositive definite kernelMercer's theorempiecewise polynomial splines

Mathematics Subject Classification ID

Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Green's functions for ordinary differential equations (34B27) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (6)

Curvilinear mesh adaptation using radial basis function interpolation and smoothing ⋮ Generalized Whittle-Matérn and polyharmonic kernels ⋮ Improved statistical models for limited datasets in uncertainty quantification using stochastic collocation ⋮ Learning with Boundary Conditions ⋮ Decomposition and reconstruction of multidimensional signals by radial functions with tension parameters ⋮ Equally spaced points are optimal for Brownian Bridge kernel interpolation

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