# Preconditioned GMRES for oscillatory integrals

Preconditioned GMRES for oscillatory integrals

Abstract: None of the existing methods for computing the oscillatory integral $\int_{a}^{b} f(x)e^{i\omega g(x)}dx$ achieve all of the following properties: high asymptotic order, stability, avoiding the computation of the path of steepest descent and insensitivity to oscillations in f. We present a new method that satisfies these properties, based on applying the GMRES algorithm to a preconditioned differential operator.

Bibliographic Details

Issue Date: 2008-11Identifiers

Urn: uuid:6e75d4f7-79a8-468e-8a86-d376d29a283a Item Description

Type: Technical Report;

Relationships

Author: Sheehan Olver - - - - Bibliographic Details Issue Date: 2008-11 - Identifiers Urn: uuid:6e75d4f7-79a8-468e-8a86-d376d29a283a - -

Source: https://ora.ox.ac.uk/objects/uuid:6e75d4f7-79a8-468e-8a86-d376d29a283a