TY - JOUR
T1 - Adaptive residual subsampling algorithms for kernel interpolation based on cross validation techniques
AU - Cavoretto, Roberto
AU - Haider, Adeeba
AU - Lancellotti, Sandro
AU - Mezzanotte, Domenico
AU - Noorizadegan, Amir
N1 - The authors sincerely thank the reviewers for their constructive and valuable comments. This work has been supported by the INdAM Research group GNCS as part of the GNCS-
INdAM 2024 project “Metodi kernel e polinomiali per l’approssimazione e l’integrazione: teoria e software applicativo”. The work of R.C. and D.M. has been supported by the Spoke 1 “FutureHPC & BigData”of ICSC - Centro Nazionale di Ricerca in High-Performance Computing, Big Data and Quantum Computing, funded by European Union - NextGenerationEU. Moreover, the work has been supported by the Fondazione CRT, project 2022 “Modelli matematici ealgoritmi predittivi di intelligenza artificiale per la mobilit`a sostenibile”. This research has been accomplished within the RITA “Research ITalian network on Approximation”, the UMI Group TAA “Approximation Theory and Applications”, and the SIMAI Activity Group ANA&A “Numerical and Analytical Approximation of Data and Functions with Applications”. The work of A.N. has financially been supported by the National Science and Technology Council of Taiwan under grant numbers 112-2811-E-002-020-MY3.
Publisher Copyright:
© 2024 Tuncer ACAR. All rights reserved.
PY - 2024/12/16
Y1 - 2024/12/16
N2 - In this article, we present an adaptive residual subsampling scheme designed for kernel based interpolation. For an optimal choice of the kernel shape parameter we consider some cross validation (CV) criteria, using efficient algorithms of k-fold CV and leave-one-out CV (LOOCV) as a special case. In this framework, the selection of the shape parameter within the residual subsampling method is totally automatic, provides highly reliable and accurate results for any kind of kernel, and guarantees existence and uniqueness of the kernel based interpolant. Numerical results show the performance of this new adaptive scheme, also giving a comparison with other computational techniques.
AB - In this article, we present an adaptive residual subsampling scheme designed for kernel based interpolation. For an optimal choice of the kernel shape parameter we consider some cross validation (CV) criteria, using efficient algorithms of k-fold CV and leave-one-out CV (LOOCV) as a special case. In this framework, the selection of the shape parameter within the residual subsampling method is totally automatic, provides highly reliable and accurate results for any kind of kernel, and guarantees existence and uniqueness of the kernel based interpolant. Numerical results show the performance of this new adaptive scheme, also giving a comparison with other computational techniques.
KW - Adaptive interpolation
KW - cross validation schemes
KW - meshfree methods
KW - radial basis function approximation
KW - shape parameter optimization
UR - https://www.scopus.com/pages/publications/85212638171
U2 - 10.33205/cma.1518603
DO - 10.33205/cma.1518603
M3 - Journal article
AN - SCOPUS:85212638171
SN - 2651-2939
VL - 7
SP - 76
EP - 92
JO - Constructive Mathematical Analysis
JF - Constructive Mathematical Analysis
ER -
