  This article discusses a more general and numerically stable Rybicki Press
algorithm, which enables inverting and computing determinants of covariance
matrices, whose elements are sums of exponentials. The algorithm is true in
exact arithmetic and relies on introducing new variables and corresponding
equations, thereby converting the matrix into a banded matrix of larger size.
Linear complexity banded algorithms for solving linear systems and computing
determinants on the larger matrix enable linear complexity algorithms for the
initial semi-separable matrix as well. Benchmarks provided illustrate the
linear scaling of the algorithm.
