TY - JOUR
T1 - Computation of quasiseparable representations of Green matrices
AU - Boito, P.
AU - Eidelman, Y.
N1 - Publisher Copyright:
© 2024 The Author(s)
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - Green matrices
KW - Inverses of banded matrices
KW - Quasiseparable structure
UR - http://www.scopus.com/inward/record.url?scp=85192817873&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2024.04.034
DO - 10.1016/j.laa.2024.04.034
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AN - SCOPUS:85192817873
SN - 0024-3795
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -