Generalizations of Nekrasov matrices and applications

• Autorzy: Ljiljana Cvetković , Vladimir Kostić , Maja Nedović
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Nekrasov matrices; H-matrices

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

wydano

2015-01-01

otrzymano

2013-12-29

zaakceptowano

2014-04-15

online

2014-10-28

Twórcy

autor

Ljiljana Cvetković

• Dept. of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Serbia, Trg Dositeja Obradovi´ca 4, 21000 Novi Sad, Serbia

autor

Vladimir Kostić

• Dept. of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Serbia, Trg Dositeja Obradovi´ca 4,21000 Novi Sad, Serbia

autor

Maja Nedović

• Dept. of Mathematics and Informatics, Faculty of Science, University of Novi Sad, Serbia, Trg Dositeja Obradovi´ca 4, 21000 Novi Sad, Serbia

Bibliografia

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• [2] Cvetkovi´c, Lj.: H-matrix theory vs. eigenvalue localization. Numer. Algor. 42(2006), 229-245.
• [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.
• [4] Cvetkovi´c, Lj., Kosti´c, V., Rauški, S., A new subclass of H-matrices. Appl. Math. Comput. 208/1(2009), 206-210.[WoS]
• [5] Gudkov, V.V.: On a certain test for nonsingularity of matrices. Latv. Mat. Ezhegodnik 1965, Zinatne, Riga (1966), 385-390.
• [6] Li, W.: On Nekrasov matrices. Linear Algebra Appl. 281(1998), 87-96.
• [7] Robert, F.: Blocs H-matrices et convergence des methodes iteratives classiques par blocs. Linear Algebra Appl. 2(1969), 223-265.[Crossref]
• [8] Szulc, T.: Some remarks on a theorem of Gudkov. Linear Algebra Appl. 225(1995), 221-235.
• [9] Varah, J. M.: A lower bound for the smallest value of a matrix. Linear Algebra Appl. 11(1975), 3-5.

Identyfikatory

DOI

10.1515/math-2015-0012