Computation of quasiseparable representations of Green matrices
arXiv:2308.02701 · doi:10.1016/j.laa.2024.04.034
Abstract
The well-known Asplund theorem states that the inverse of a (possibly one-sided) band matrix is a Green matrix. In accordance with quasiseparable theory, such a matrix admits a quasiseparable representation in its rank-structured part. Based on this idea, we derive algorithms that compute a quasiseparable representation of with linear complexity. Many inversion algorithms for band matrices exist in the literature. However, algorithms based on a computation of the rank structure performed theoretically via the Asplund theorem appear for the first time in this paper. Numerical experiments confirm complexity estimates and offer insight into stability properties.