On the numerical quadrature of highly-oscillating integrals II: Irregular oscillators

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On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation (2006, methodology): “Methods have been devised that compute an accurate approximation to the value of the integral with low computational complexity and with a number of operations that actually decreases as ω increases to infinity [12, 13, 14, 15, 16, 17, 18].”
From high oscillation to rapid approximation I: Modified Fourier expansions (2008, background): “The reason is that Filon-type methods are far superior for small values ofn, before the onset of ‘proper’ asymptotic behaviour, since they exhibit high conventional order of approximation for low frequencies (Iserles 2004).”
Stability and error estimates for Filon–Clenshaw–Curtis rules for highly oscillatory integrals (2011, unknown): “For example [14] concerned (among other things) the case when the oscillatory factor in (1) is replaced with exp(ikh(x)), while [15] obtained methods which converged with higher negative powers of k by using interpolation of derivatives at the end points of the domain of integration.”