Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices
نویسندگان
چکیده
We present new comparison theorems for the spectral radii of matrices arising from splittings of different matrices under nonnegativity assumptions. Our focus is on establishing strict inequalities of the spectral radii without imposing strict inequalities of the matrices, but we also obtain new results for nonstrict inequalities of the spectral radii. We emphasize two different approaches, one combinatorial and the other analytic and discuss their merits in the light of the results obtained. We try to get fairly general results and indicate by counter-examples that some of our hypotheses cannot be relaxed in certain directions. © 2001 Elsevier Science Inc. All rights reserved. AMS classification: 65F10; 15A06; 15A48
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تاریخ انتشار 2001