Computation of quasiseparable representations of Green matrices
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The well-known Asplund theorem states that the inverse of a (possibly one-sided) band matrix A 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 A^-1 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.
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