Table 2.

The parameters of the optimal models in Example 2: time-scale factors $\alpha$, numbers of model summands $K$, regularization parameter ${\lambda }_{GCV}$, optimal model parameters ${\stackrel{-}{\mathit{g}}}_K^{{\lambda }_{GCV}}$, approximation error indices: identification index $Q_N\left({\stackrel{-}{\mathit{g}}}_K^{{\lambda }_{GCV}}\right)$, Equation (10), the errors $ERR$ (60) of the relaxation spectrum models.

Model	$\mathit{K}$	$\mathit{\alpha }$ $\mathbf{\left[}\mathit{s}\mathbf{\right]}$	${\mathit{\lambda }}_{\mathit{G}\mathit{C}\mathit{V}}$ $\mathbf{[}\mathbf{-}\mathbf{]}$	${\mathit{Q}}_{\mathit{N}}\left({\stackrel{-}{\mathit{g}}}_{\mathit{K}}^{{\mathit{\lambda }}_{\mathit{G}\mathit{C}\mathit{V}}}\right)$ $\mathbf{\left[}{\mathit{M}\mathit{P}\mathit{a}}^2\mathbf{\right]}$	${\mathbf{\Vert }{\stackrel{-}{\mathit{g}}}_{\mathit{K}}^{\mathit{\lambda }}\mathbf{\Vert }}_2$ $\mathbf{\left[}\mathit{M}\mathit{P}\mathit{a}·{\mathit{s}}^{1/2}\mathbf{\right]}$	${\mathbf{\Vert }{\stackrel{-}{\mathit{H}}}_{\mathit{K}}^{\mathit{M}}\left(\mathit{v}\right)\mathbf{\Vert }}_2$ $\mathbf{\left[}\mathit{M}\mathit{P}\mathit{a}·{\mathit{s}}^{1/2}\mathbf{\right]}$	$\mathit{E}\mathit{R}\mathit{R}$ $\left[\mathit{M}\mathit{P}\mathit{a}·{\mathit{s}}^{1/2}\right]$
Legendre model	6	950	2.72 × 10−6	0.003261	62.717	62.717	80.604
	8	620	4.968 × 10−6	0.00135	58.9351	58.9351	79.7444
	10	500	6.372 × 10−6	0.0007138	57.4422	57.4422	79.7170
	12	400	7.754 × 10−6	0.000557	56.8251	56.8251	79.7917
	14	300	9.226 × 10−6	0.000575	56.6390	56.6390	79.8353
Laguerre model	8	8500	2.524 × 10−6	0.002722	63.0250	63.0250	82.4674
	10	8000	3.668 × 10−6	0.001494	59.7092	59.7092	81.0828
	12	7500	4.840 × 10−6	0.0009379	58.3032	58.3032	80.6344
	14	8000	5.294 × 10−6	0.000711	57.3277	57.3277	80.3069
	16	6000	7.498 × 10−6	0.000699	57.39886	57.39886	80.4441
	18	6500	7.686 × 10−6	0.000527	56.7967	56.7967	80.1877
Chebyshev model	6	31,000	6.0 × 10−7	0.8259	289.32	289.32
	8	31,500	6.0 × 10−7	0.7115	346.30	346.30
	10	32,000	5.0 × 10−7	0.6504	376.6564	376.66
	12	33,000	5.0 × 10−7	0.6344	379.0402	379.04
	14	33,000	5.0 × 10−7	0.6029	375.3072	375.31
	16	34,500	5.0 × 10−7	0.6136	382.0129	382.01
Hermite model	6	27,000	1.8 × 10−6	3.0971	390.24	387.13
	8	26,800	1.6 × 10−6	2.1911	452.31	445.67
	10	26,750	1.6 × 10−6	1.9010	440.42	436.32
	12	26,700	1.8 × 10−6	1.8148	389.93	378.76
	14	26,600	0.999 × 10−6	2.9235	472.33	467.32
	16	26,600	0.994 × 10−6	2.7767	467.45	461.56