Kernel-Based Approximation Methods for Partial Differential Equations: Deterministic or Stochastic Problems?

DOI10.1007/978-3-319-59912-0_19zbMath1385.65012OpenAlexW2737513277MaRDI QIDQ4609813

Qi Ye

Publication date: 26 March 2018

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

Full work available at URL: https://doi.org/10.1007/978-3-319-59912-0_19

zbMATH Keywords

numerical experimentsHermite-Birkhoff interpolationGaussian process regressionpositive definite kernelkernel-based approximation methodkernel-based probability spacemultiple Poisson equation

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (4)

A trustable shape parameter in the kernel-based collocation method with application to pricing financial options ⋮ Kernel-based probability measures for interpolations ⋮ Kernel-based probability measures for generalized interpolations: a deterministic or stochastic problem? ⋮ Quasi-interpolation for multivariate density estimation on bounded domain

Uses Software

• Matlab
• GaussQR

Cites Work

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• Interpolation of spatial data – A stochastic or a deterministic problem?
• A Kernel-Based Collocation Method for Elliptic Partial Differential Equations With Random Coefficients
• Kernel-based Approximation Methods using MATLAB
• Accurate Uncertainty Quantification Using Inaccurate Computational Models
• Support Vector Machines
• Gaussian Hilbert Spaces
• Conditional Confidence Statements and Confidence Estimators
• Radial Basis Functions
• Approximation of stochastic partial differential equations by a kernel-based collocation method
• Scattered Data Approximation

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