Fast Computation of Singular Oscillatory Fourier Transforms

Table 3

Absolute errors in 𝑛-point approximations by the proposed method to the integral ∫³₂(𝑥−2)^−(1/2)(3−𝑥)^−(1/2)sin𝑥𝑒^𝑖𝜔𝑥𝑑𝑥.

𝜔⧵𝑛	2	3	4
8	4.5×10^−5	2.8×10^−6	3.0×10^−7
16	2.4×10^−6	5.2×10^−8	1.8×10^−9
32	1.1×10^−7	6.2×10^−10	6.7×10^−12
64	5.2×10^−9	7.7×10^−12	2.5×10^−14