Published 1995 | Version v1
Book section Metadata-only

Structured matrices and inverses

Comon, Pierre
Others:
Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
A. Bojanczyk and G. Cybenko

Description

A matrix (and any associated linear system) will be referred to as structured if it has a small displacement rank. It is known that the inverse of a structured matrix is structured, which allows fast inversion (or solution), and reduced storage requirements. According to two definitions of displacement structure of practical interest, it is shown here that several types of inverses are also structured, including the Moore-Penrose inverse of rank-deficient matrices.

Additional details

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Created:
February 28, 2023
Modified:
November 22, 2023