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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