Computation of quasiseparable representations of Green matrices

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 quasis...

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Bibliographic Details
Published in:Linear algebra and its applications 2024-05
Main Authors: Boito, P., Eidelman, Y.
Format: Article
Language:English
Subjects:
Green matrices
Inverses of banded matrices
Quasiseparable structure
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Summary: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2024.04.034