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The p-norm of circulant matrices [r-libre/2385]

Bouthat, Ludovick; Khare, Apoorva; Mashreghi, Javad, & Morneau-Guérin, Frédéric (2022). The p-norm of circulant matrices. Linear and Multilinear Algebra, 70 (21), 7176-7188. https://doi.org/10.1080/03081087.2021.1983513

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Content : Accepted Version
Item Type: Journal Articles
Refereed: Yes
Status: Published
Abstract: In this note we study the induced p-norm of circulant matrices A(n,+/- a, b), acting as operators on the Euclidean space R^n. For circulant matrices whose entries are nonnegative real numbers, in particular for A(n,a,b), we provide an explicit formula for the p-norm, for p between 1 and infinity. The calculation for A(n,-a,b) is more complex. The 2-norm is precisely determined. As for the other values of p, two different categories of upper and lower bounds are obtained. These bounds are optimal at the end points (i.e. p=1 and p = infinity) as well as at p = 2.
Official URL: https://www.tandfonline.com/doi/full/10.1080/03081...
Depositor: Morneau-Guérin, Frédéric
Owner / Manager: Frédéric Morneau-Guérin
Deposited: 09 Sep 2021 14:23
Last Modified: 19 Apr 2023 13:52

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