Table 1.

Spectral condition numbers $\kappa \left({\mathit{\Phi }}_K\right)$ and $\kappa \left({\mathit{\Phi }}_K+\alpha \lambda {\mathbb{I}}_{K,K}\right)$ defined according to (30).

$\mathit{\alpha }\mathit{\lambda }$	$\mathit{K}$ = 2	$\mathit{K}$ = 3	$\mathit{K}$ = 4	$\mathit{K}$ = 5	$\mathit{K}$ = 8	$\mathit{K}$ = 10	$\mathit{K}$ = 15	$\mathit{K}$ = 20	$\mathit{K}$ = 100	$\mathit{K}$ = 1000	$\mathit{K}$ = 10,000
0	38.474	1.35 × 103	4.59 × 104	1.54 × 106	5.64 × 1010	6.23 × 1013	2.61 × 1017	6.45 × 1018	1.20 × 1019	9.59 × 1020	1.0 × 1022
10	1.071	1.087	1.098	1.106	1.122	1.129	1.14129	1.1496	1.18809	1.225	1.248
1	1.699	1.874	1.977	2.056	2.215	2.288	2.412	2.495	2.880	3.247	3.479
0.1	6.983	9.688	10.773	11.559	13.154	13.877	15.123	15.953	19.800	23.469	25.798
0.01	25.552	83.135	98.55	106.59	122.542	129.766	142.232	150.535	189.001	225.687	248.977
1 × 10−3	36.600	532.056	958.14	1.06 × 103	1.22 × 103	1.29 × 103	1.41 × 103	1.49 × 103	1.88 × 103	2.25 × 103	2.48 × 103
1 × 10−4	38.278	1.17 × 103	8.06 × 103	1.05 × 104	1.22 × 104	1.29 × 104	1.41 × 104	1.49 × 104	1.88 × 104	2.25 × 104	2.48 × 104
1 × 10−5	38.454	1.33× 103	3.12 × 104	9.88 × 104	1.22 × 105	1.29 × 105	1.41 × 105	1.49 × 105	1.88 × 105	2.25 × 105	2.48 × 105