Theory and Modern Applications
Table 2 The RMS values (32) for \(p\in \{0,0.01\%,0.1\%\}\) and \(\beta \in \{0,10^{-12},10^{-11},10^{-10}, 10^{-9},10^{-8},10^{-7}\}\) for Tests 1 and 2
Test 1 | Test 2 | ||||||
|---|---|---|---|---|---|---|---|
p | β | RMS(α) | Minimum value of \(\mathbb{F}\) or \(\mathbb{F}_{\beta }\) | p | β | RMS(α) | Minimum value of \(\mathbb{F}\) or \(\mathbb{F}_{\beta }\) |
0 | 0 | 0.0868 | \(\mathbb{F}=2.4\mbox{E}{-}30\) | 0 | 0 | 0.0872 | \(\mathbb{F}=8.1\mbox{E}{-}30\) |
0.01% | 0 | 3.4204 | \(\mathbb{F}=1.3\mbox{E}{-}29\) | 0.01% | 0 | 3.3676 | \(\mathbb{F}=8.5\mbox{E}{-}30\) |
10−10 | 0.0790 | \(\mathbb{F}_{\beta }=1.1\mbox{E}{-}7\) | 10−12 | 0.2368 | \(\mathbb{F}_{\beta }=7.1\mbox{E}{-}8\) | ||
10−9 | 0.0776 | \(\mathbb{F}_{\beta }=4.2\mbox{E}{-}7\) | 10−11 | 0.1245 | \(\mathbb{F}_{\beta }=2.3\mbox{E}{-}7\) | ||
10−8 | 0.0982 | \(\mathbb{F}_{\beta }=3.2\mbox{E}{-}6\) | 10−10 | 0.2728 | \(\mathbb{F}_{\beta }=1.5\mbox{E}{-}6\) | ||
0.1% | 0 | 34.2297 | \(\mathbb{F}=1.3\mbox{E}{-}29\) | 0.1% | 0 | 33.9465 | \(\mathbb{F}=2.1\mbox{E}{-}29\) |
10−9 | 0.1573 | \(\mathbb{F}_{\beta }=8.4\mbox{E}{-}6\) | 10−11 | 0.8454 | \(\mathbb{F}_{\beta }=6.7\mbox{E}{-}6\) | ||
10−8 | 0.1100 | \(\mathbb{F}_{\beta }=1.1\mbox{E}{-}5\) | 10−10 | 0.5282 | \(\mathbb{F}_{\beta }=8.6\mbox{E}{-}6\) | ||
10−7 | 0.1701 | \(\mathbb{F}_{\beta }=3.6\mbox{E}{-}5\) | 10−9 | 0.6936 | \(\mathbb{F}_{\beta }=1.6\mbox{E}{-}5\) | ||