Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access October 28, 2014

Generalizations of Nekrasov matrices and applications

  • Ljiljana Cvetković , Vladimir Kostić and Maja Nedović EMAIL logo
From the journal Open Mathematics

Abstract

In this paper we present a nonsingularity result which is a generalization of Nekrasov property by using two different permutations of the index set. The main motivation comes from the following observation: matrices that are Nekrasov matrices up to the same permutations of rows and columns, are nonsingular. But, testing all the permutations of the index set for the given matrix is too expensive. So, in some cases, our new nonsingularity criterion allows us to use the results already calculated in order to conclude that the given matrix is nonsingular. Also, we present new max-norm bounds for the inverse matrix and illustrate these results by numerical examples, comparing the results to some already known bounds for Nekrasov matrices.

References

[1] Berman, A., Plemmons, R.J.: Nonnegative matrices in the mathematical sciences. Classics in Applied Mathematics, vol. 9, SIAM, Philadelphia, 1994.10.1137/1.9781611971262Search in Google Scholar

[2] Cvetkovi´c, Lj.: H-matrix theory vs. eigenvalue localization. Numer. Algor. 42(2006), 229-245.Search in Google Scholar

[3] Cvetkovi´c, Lj, Ping-Fan Dai, Doroslovaˇcki, K., Yao-Tang Li: Infinity norm bounds for the inverse of Nekrasov matrices. Appl. Math. Comput. 219, 10 (2013), 5020-5024.Search in Google Scholar

[4] Cvetkovi´c, Lj., Kosti´c, V., Rauški, S., A new subclass of H-matrices. Appl. Math. Comput. 208/1(2009), 206-210.10.1016/j.amc.2008.11.037Search in Google Scholar

[5] Gudkov, V.V.: On a certain test for nonsingularity of matrices. Latv. Mat. Ezhegodnik 1965, Zinatne, Riga (1966), 385-390.Search in Google Scholar

[6] Li, W.: On Nekrasov matrices. Linear Algebra Appl. 281(1998), 87-96.Search in Google Scholar

[7] Robert, F.: Blocs H-matrices et convergence des methodes iteratives classiques par blocs. Linear Algebra Appl. 2(1969), 223-265.Search in Google Scholar

[8] Szulc, T.: Some remarks on a theorem of Gudkov. Linear Algebra Appl. 225(1995), 221-235.Search in Google Scholar

[9] Varah, J. M.: A lower bound for the smallest value of a matrix. Linear Algebra Appl. 11(1975), 3-5.Search in Google Scholar

Received: 2013-12-29
Accepted: 2014-4-15
Published Online: 2014-10-28
Published in Print: 2015-1-1

© 2015 Ljiljana Cvetković et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 28.2.2024 from https://www.degruyter.com/document/doi/10.1515/math-2015-0012/html
Scroll to top button