Fast Evaluation of Canonical Oscillatory Integrals

Fast evaluation of oscillatory integrals is an issue attracts much attention in many fields. In this paper, we are interested in the calculation of canonical oscillatory integrals, and the irregular oscillatory integrals are transformed into canonical ones with respect to the presences of stationary phase points or not. An improved-Levin method is proposed to calculated the canonical oscillatory integral, where the eigen-decomposition is employed to solve the target system of linear equation, and a much higher efficiency is yielded in comparison with the direct solution methods such as the Gaussian elimination