Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices

Elsner L, Frommer A, Nabben R, Schneider H, Szyld DB (2003)
Linear Algebra and its Applications 363: 65-80.

Konferenzbeitrag | Veröffentlicht | Englisch
 
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Autor*in
Elsner, LudwigUniBi; Frommer, Andreas; Nabben, Reinhard; Schneider, Hans; Szyld, Daniel B.
Abstract / Bemerkung
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. (C) 2001 Elsevier Science Inc. All rights reserved.
Stichworte
nonnegative; matrices; iterative solution of linear systems; Perron-Frobenius theory; combinatorial matrix theory; strict comparison theorems
Erscheinungsjahr
2003
Band
363
Seite(n)
65-80
ISSN
0024-3795
Page URI
https://pub.uni-bielefeld.de/record/1612430

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Elsner L, Frommer A, Nabben R, Schneider H, Szyld DB. Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices. Linear Algebra and its Applications. 2003;363:65-80.
Elsner, L., Frommer, A., Nabben, R., Schneider, H., & Szyld, D. B. (2003). Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices. Linear Algebra and its Applications, 363, 65-80. doi:10.1016/S0024-3795(01)00535-3
Elsner, L., Frommer, A., Nabben, R., Schneider, H., and Szyld, D. B. (2003). Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices. Linear Algebra and its Applications 363, 65-80.
Elsner, L., et al., 2003. Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices. Linear Algebra and its Applications, 363, p 65-80.
L. Elsner, et al., “Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices”, Linear Algebra and its Applications, vol. 363, 2003, pp. 65-80.
Elsner, L., Frommer, A., Nabben, R., Schneider, H., Szyld, D.B.: Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices. Linear Algebra and its Applications. 363, 65-80 (2003).
Elsner, Ludwig, Frommer, Andreas, Nabben, Reinhard, Schneider, Hans, and Szyld, Daniel B. “Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices”. Linear Algebra and its Applications 363 (2003): 65-80.