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arXiv · 2308.02701

Computation of quasiseparable representations of Green matrices

Paola Boito·Yuli Eidelman
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Abstract

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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Paola Boito, Yuli Eidelman. 2023-08-04. Computation of quasiseparable representations of Green matrices. https://doi.org/10.1016/j.laa.2024.04.034

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