TY - JOUR
TI - The adaptation of the cross validation aproach for RBF-based collocation methods
AU - Krowiak, Artur
AU - Podgórski, Jordan
TI - The adaptation of the cross validation aproach for RBF-based collocation methods
AB - 
	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.
VL - 2017
IS - Volume 7 Year 2017 (114)
PY - 2017
SN - 0011-4561
C1 - 2353-737X
SP - 147
EP - 156
DO - 10.4467/2353737XCT.17.115.6656
UR - https://ejournals.eu/en/journal/czasopismo-techniczne/article/the-adaptation-of-the-cross-validation-aproach-for-rbf-based-collocation-methods
KW - radial basis functions
KW - shape parameter
KW - cross-validation approach