2014
DOI: 10.1016/j.compstruct.2013.07.041
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Energy based approach for shape parameter selection in radial basis functions collocation method

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Cited by 18 publications
(7 citation statements)
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“…MQ-RBF's includes the user-defined shape parameter c, which has an influence on accuracy and stability of the solution [37,38,39]. Some of the most popular RBFs function are listed in table 1.…”
Section: Radial Basis Function (Rbf)mentioning
confidence: 99%
“…MQ-RBF's includes the user-defined shape parameter c, which has an influence on accuracy and stability of the solution [37,38,39]. Some of the most popular RBFs function are listed in table 1.…”
Section: Radial Basis Function (Rbf)mentioning
confidence: 99%
“…As stated above, the choice of a suitable value of the shape parameter in the infinitely smooth RBFs is very important and has been an ongoing challenge problem. Up to now, no mathematical theory has been developed to rule the selection of an adequate value but only several approaches are available in the open literature [7][8][9][10][11]. In the early works, many researchers tried to present some empirical formulas based on the number and distribution of data points to select a good value for the shape parameter; see [12][13][14] for examples.…”
Section: Introductionmentioning
confidence: 99%
“…Recently, some improvements of the LOOCV algorithm have been deeply studied; see [16][17][18][19][20] and references therein. Other techniques for finding the optimal shape parameter include the energy-based method [7,9], the sample solution approach [10], the interval method [21], and so on. Another type of technique [22,23], i.e., bypassing the problem of the optimal shape parameter selection by reducing its influence on the stability of the method, is also of great interest.…”
Section: Introductionmentioning
confidence: 99%
“…Bayona (2011, 2012) [ 40 , 41 ] has attempted to find optimal constant and variable shape parameters for the multiquadric approximation method combined with the finite difference method. Tsai et al (2010) [ 42 ] proposed the golden section algorithm, Esmaeilbeigi and Hosseini (2014) [ 43 ] the genetic algorithm, Iurlaro et al (2014) [ 44 ] the energy-based approach, and Chen et al (2010) [ 14 ] the sample solution approach. Despite the very intensive development of methods for finding a good value of the shape parameter in the recent years, the choice of the shape parameter for multiply-connected, complex-shaped domain problems remains an open problem [ 14 ].…”
Section: Introductionmentioning
confidence: 99%