Extrapolation methods and nonlinear transformations for applied mathematics,theoretical chemistry and molecular physics

高振荡积分在量子化学、图像分析、电动力学、计算机断层扫描和流体力学等各种应用中发挥着重要作用。传统的求积分规则无法准确、快速地对这些积分进行数值计算。很少有外推方法适合于高振荡积分，特别是D和G变换。然而，这些方法的应用可能是极其困难的，需要大量的计算。开发新的算法来计算这些高振荡积分的方法是至关重要的。

Highly oscillatory integrals play a major role in various applications, e.g. quantum chemistry, image analysis, electrodynamics, computerized tomography and fluid mechanics. Traditional quadrature rules have failed in the accurate and rapid numerical evaluation of these integrals. Few classes of extrapolation methods are well suited for highly oscillatory integrals, notably the D and G transformations. However, the application of these methods can be extremely difficult and require a large amount of calculation. The development of new algorithms for the computation of these methods for highly oscillatory integrals is critical.