JordanRotate.m

It is possible that the user can provide unbounded endpoints \(a\) and/or \(b\) which do not precisely correspond to valleys, but still enjoy exponential decay. This subroutine relies on ideas from Jordan’s Lemma: the complex argument of unbounded endpoints can be rotated a little without affecting the value of the integral. When possible, the subroutine rotates the argument of unbounded endpoints \(a,b\) to the nearest valley of the phase function \(g\).

[a,b] = JordanRotate(a,b,valleys,Params)

Note that only infinite endpoints are rotated - as this does not change the value of the integral.

Inputs

• a and b: The original endpoints, before rotation.

• valleys: The valleys of the polynomial phase function \(g\).

• Params: A Matlab struct of parameters, including information about which endpoints are infinite.

Outputs

• a and b: The endpoints after rotation.