<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The paper shows the adaptation of the cross validation approach, known from interpolation problems, for estimating the value of a shape parameter for radial basis functions. The latter are involved in two collocation techniques used on an unstructured grid to find approximate solution of differential equations. To obtain accurate results, the shape parameter should be chosen as a result of a trade-off between accuracy and conditioning of the system. The cross validation approach called “leave one out” takes these aspects into consideration. The numerical examples that summarize the investigations show the usefulness of the approach.</p></abstract>

The paper shows the adaptation of the cross validation approach, known from interpolation problems, for estimating the value of a shape parameter for radial basis functions. The latter are involved in two collocation techniques used on an unstructured grid to find approximate solution of differential equations. To obtain accurate results, the shape parameter should be chosen as a result of a trade-off between accuracy and conditioning of the system. The cross validation approach called “leave one out” takes these aspects into consideration. The numerical examples that summarize the investigations show the usefulness of the approach.

The Adaptation of the Cross Validation Aproach for RBF-Based Collocation Methods

Institute of Computer Science, Faculty of Mechanical Engineering

Technical Transactions

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Public License.

{"article-title":"The Adaptation of the Cross Validation Aproach for RBF-Based Collocation Methods"}

The paper shows the adaptation of the cross validation approach, known from interpolation problems, for estimating the value of a shape parameter for radial...

The Adaptation of the Cross Validation Aproach for RBF-Based Collocation Methods

Published Online: May 26, 2020

Page range: 147 - 156

DOI: https://doi.org/10.4467/2353737XCT.17.115.6656

Keywords
radial basis functions, shape parameter, cross-validation approach

© 2020 Artur Krowiak et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Public License.

The Adaptation of the Cross Validation Aproach for RBF-Based Collocation Methods

Published Online: May 26, 2020

Page range: 147 - 156

DOI: https://doi.org/10.4467/2353737XCT.17.115.6656

Keywordsradial basis functions, shape parameter, cross-validation approach

© 2020 Artur Krowiak et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Public License.

Keywords
radial basis functions, shape parameter, cross-validation approach