  Implementation of many statistical methods for large, multivariate data sets
requires one to solve a linear system that, depending on the method, is of the
dimension of the number of observations or each individual data vector. This is
often the limiting factor in scaling the method with data size and complexity.
In this paper we illustrate the use of Krylov subspace methods to address this
issue in a statistical solution to a source separation problem in cosmology
where the data size is prohibitively large for direct solution of the required
system. Two distinct approaches, adapted from techniques in the literature, are
described: one that uses the method of conjugate gradients directly to the
Kronecker-structured problem and another that reformulates the system as a
Sylvester matrix equation. We show that both approaches produce an accurate
solution within an acceptable computation time and with practical memory
requirements for the data size that is currently available.
