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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)