A fast and stable method for rotating spherical harmonic expansions
spherical harmonic expansion. This is a well-studied problem, arising
in classical scattering theory, quantum mechanics and numerical
analysis, usually addressed through the explicit construction of the
Wigner rotation matrices. Existing fast algorithms, based on
recurrence relations, are subject to a variety of instabilities,
limiting the effectiveness of the approach for expansions of high
We show that rotation can be carried out easily and stably
through pseudospectral projection, without ever constructing the
matrix entries themselves. In the simplest version of the method,
projection is carried out on the equator of the rotated sphere. If
only the lowest angular modes are required, the algorithm can be
further accelerated by using a sequence of constant latitude circles.
This is joint work with Leslie Greengard.