title: Karhunen-Loeve decomposition in the presence of symmetry. I.
abstract: The Karhunen-Loève (KL) decomposition is widely used for data which very often exhibit some symmetry, afforded by a group action. For a finite group, we derive an algorithm using group representation theory to reduce the cost of determining the KL basis. We demonstrate the technique on a Lorenz-type ODE system. For a compact group such as tori or SO(3,R) the method also applies, and we extend results to these cases. As a short example, we consider the circle group S(1).
authors.affiliation: Dept. of Math., Arizona Univ., Tucson, AZ 85721, USA.
authors.forename: B
authors.initials: B
authors.lastname: Lahme
authors.forename: R
authors.initials: R
authors.lastname: Miranda