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Table 3 Result of optimization of the Kriging parameters by resolving the log-likelihood function with respect to the shape parameter theta and the regularization parameter for no polynomial and polynomial degree equals to 0, 1, 2 and 3

From: Low dimensional modeling of Double T-junctions in water distribution networks using Kriging interpolation and Delaunay triangulation

Polynomial degree No polynomial k = 0 k = 1 k = 2 k = 3
\( \tilde{\uptheta} \) 2.76 2.81 2.85 3.13 3.63
α 0.5 0.5 0.5 0.5 0.5
\( \mathrm{f}\left(\tilde{\uptheta},\upalpha \right) \) initial 2902.92 2895.64 2891.3 2855.29 2806.2
\( \mathrm{f}\left(\tilde{\uptheta},\upalpha \right) \) optimal 2866.93 2864.77 2863.32 2841.27 2804.62
average error   1.75 1.94 1.86 1.82
standard deviation   3.40 3.24 2.83 2.37
min   0.02 0 0 0
max   35.19 34.09 31.4 26.86