2023/08/04 by Paola Boito, Boito, Paola, Yuli Eidelman +1 · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2308.02701
openalex publication_date 2023/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
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.