Table 2 The absolute values for the error (55) of the optimal quadrature formula (54) for \(N=1, 10, 100, 1000\) and \(\omega =1.1, 10.1, 100.1, 1000.1\)
From: Optimal quadrature formulas for oscillatory integrals in the Sobolev space
ω = 1.1 | ω = 10.1 | ω = 100.1 | ω = 1000.1 | |
|---|---|---|---|---|
\(|I-A_{\mathrm{opt}}|\) | \(|I-A_{\mathrm{opt}}|\) | \(|I-A_{\mathrm{opt}}|\) | \(|I-A_{\mathrm{opt}}|\) | |
N = 1 | 1.114784(−2) | 1.444594(−4) | 1.484368(−6) | 1.488425(−8) |
N = 10 | 3.025851(−5) | 6.946015(−6) | 8.425457(−8) | 8.578893(−10) |
N = 100 | 2.843105(−8) | 3.005545(−8) | 7.045133(−9) | 8.440393(−11) |
N = 1000 | 2.845974(−11) | 2.842208(−11) | 3.003591(−11) | 7.055061(−12) |