A Robust and Accurate Quasi-Monte Carlo Algorithm for Estimating Eigenvalue of Homogeneous Integral Equations

Table 1

Relatives errors, STD, and 𝜆.

Method	Number of simulation		Example 4			Example 5
		STD	𝜆	Relative error	STD	𝜆	Relative error
NMC	𝑁=100	0.1060	1.1526	0.1526	0.1307	1.3568	0.0656
AVMC	𝑁=100	0.0743	1.0446	0.0446	0.0996	1.3424	0.0543
AVQMC	𝑁=100	0.0885	1.0055	0.0055	0.1486	1.2733	4.5863×10^−5
NMC	𝑁=500	0.0579	1.0242	0.0242	0.0856	1.2997	0.0208
AVMC	𝑁=500	0.0390	1.0110	0.0110	0.0554	1.2632	0.0079
AVQMC	𝑁=500	0.0439	1.0010	0.0010	0.0681	1.2752	0.0016
NMC	𝑁=1000	0.0447	0.9541	0.0459	0.1307	1.2972	0.0188
AVMC	𝑁=1000	0.0743	0.9934	0.0066	0.0931	1.2673	0.0046
AVQMC	𝑁=1000	0.0324	1.0015	0.0015	0.0497	1.2749	0.0013