The extension of Rippa's algorithm beyond LOOCV

DOI10.1016/j.aml.2021.107262OpenAlexW3143295495MaRDI QIDQ2233309

Yanyan Li

Publication date: 15 October 2021

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2021.107262

zbMATH Keywords

cross validationparameter tuningRBF interpolationextended Rippa's methodRippa's algorithm

Mathematics Subject Classification ID

Numerical interpolation (65D05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05) Algorithms for approximation of functions (65D15) Numerical radial basis function approximation (65D12)

Related Items (11)

A stochastic extended Rippa's algorithm for LpOCV ⋮ Efficient reduced basis algorithm (ERBA) for kernel-based approximation ⋮ Adaptive LOOCV-based kernel methods for solving time-dependent BVPs ⋮ Stabilized interpolation using radial basis functions augmented with selected radial polynomials ⋮ Bayesian approach for radial kernel parameter tuning ⋮ Data-Driven Kernel Designs for Optimized Greedy Schemes: A Machine Learning Perspective ⋮ On the selection of a better radial basis function and its shape parameter in interpolation problems ⋮ Learning via variably scaled kernels ⋮ RBFCUB: a numerical package for near-optimal meshless cubature on general polygons ⋮ Adaptive selection strategy of shape parameters for LRBF for solving partial differential equations ⋮ A compact radial basis function partition of unity method

Uses Software

• Matlab
• GaussQR

Cites Work

• Unnamed Item
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• An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
• On the search of the shape parameter in radial basis functions using univariate global optimization methods
• Jumping with variably scaled discontinuous kernels (VSDKs)
• On choosing ``optimal shape parameters for RBF approximation
• The Runge phenomenon and spatially variable shape parameters in RBF interpolation
• Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
• Shape-Driven Interpolation With Discontinuous Kernels: Error Analysis, Edge Extraction, and Applications in Magnetic Particle Imaging
• Interpolation with variably scaled kernels
• Scattered Data Approximation

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