1. bookVolume 114 (2017): Issue 7 (July 2017)
Journal Details
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Journal
eISSN
2353-737X
First Published
20 May 2020
Publication timeframe
1 time per year
Languages
English
access type Open Access

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

Published Online: 26 May 2020
Volume & Issue: Volume 114 (2017) - Issue 7 (July 2017)
Page range: 147 - 156
Journal Details
License
Format
Journal
eISSN
2353-737X
First Published
20 May 2020
Publication timeframe
1 time per year
Languages
English
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.

Keywords

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