|Publisher DOI:||10.1016/j.laa.2022.08.011||Title:||Entrywise lower and upper bounds for the Perron vector||Language:||English||Authors:||Rump, Siegfried M.||Keywords:||M-matrix; Perron vector; Perron-Frobenius theory||Issue Date:||15-Nov-2022||Source:||Linear Algebra and Its Applications 653 : 314-319 (2022-11-15)||Abstract (english):||
Let an irreducible nonnegative matrix A and a positive vector x be given. Assume αx≤Ax≤βx for some 0<α≤β∈R. Then, by Perron-Frobenius theory, α and β are lower and upper bounds for the Perron root of A. As for the Perron vector x⁎, only bounds for the ratio γ:=maxi,jxi⁎/xj⁎ are known, but no error bounds against some given vector x. In this note we close this gap. For a given positive vector x and provided that α and β as above are not too far apart, we prove entrywise lower and upper bounds of the relative error of x to the Perron vector of A.
|URI:||http://hdl.handle.net/11420/13570||ISSN:||0024-3795||Journal:||Linear algebra and its applications||Institute:||Zuverlässiges Rechnen E-19 (H)||Document Type:||Article|
|Appears in Collections:||Publications without fulltext|
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