Shifted GMRES for oscillatory integrals
By applying the generalized minimal residual (GMRES) algorithm to a shifted linear differential operator, the author constructs a new method for approximating the oscillatory integral \(\int_a^b f(x)e^{i\omega g(x)}dx\). Unlike the existing methods, this one satisfies simultaneously the following properties: it has high asymptotic order and stability, it avoids the distortions in the complex plane and it remains accurate when the integrand has oscillations at multiple scales.
generalized minimal residual (GMRES) algorithm
scientific article