Optimal designs of positive definite kernels for scattered data approximation

DOI10.1016/j.acha.2015.08.009zbMath1357.46069OpenAlexW1176528776MaRDI QIDQ285543

Qi Ye

Publication date: 19 May 2016

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2015.08.009

zbMATH Keywords

Sobolev spaceGaussian kernelGaussian fieldkernel-based approximationkernel-based probabilitymeshfree methodnormal random variableoptimal shape parameterpositive definite kernel

Mathematics Subject Classification ID

Gaussian processes (60G15) Stochastic approximation (62L20) Numerical interpolation (65D05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Applications of functional analysis in probability theory and statistics (46N30)

Related Items (8)

Generalizations of Simple Kriging Methods in Spatial Data Analysis ⋮ A trustable shape parameter in the kernel-based collocation method with application to pricing financial options ⋮ Summation of Gaussian shifts as Jacobi's third theta function ⋮ Kernel-based probability measures for interpolations ⋮ Kernel-Based Approximation Methods for Partial Differential Equations: Deterministic or Stochastic Problems? ⋮ On meshfree numerical differentiation ⋮ Generalized regularized least-squares approximation of noisy data with application to stochastic PDEs ⋮ Kernel-based probability measures for generalized interpolations: a deterministic or stochastic problem?

Uses Software

• Matlab

Cites Work

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• Reproducing kernels of Sobolev spaces via a Green kernel approach with differential operators and boundary operators
• Stochastic processes with sample paths in reproducing kernel Hilbert spaces
• Interpolation of spatial data – A stochastic or a deterministic problem?
• On Dimension-independent Rates of Convergence for Function Approximation with Gaussian Kernels
• Stable Evaluation of Gaussian Radial Basis Function Interpolants
• Support Vector Machines
• Radial Basis Functions
• Approximation of stochastic partial differential equations by a kernel-based collocation method
• Scattered Data Approximation
• Stochastic differential equations. An introduction with applications.

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