Characterization of α1 and α2-matrices

• Autorzy: Rafael Bru , Ljiljana Cvetković , Vladimir Kostić , Francisco Pedroche
• Języki publikacji: EN

Abstrakty

EN

This paper deals with some properties of α1-matrices and α2-matrices which are subclasses of nonsingular H-matrices. In particular, new characterizations of these two subclasses are given, and then used for proving algebraic properties related to subdirect sums and Hadamard products.

Słowa kluczowe

EN

H-matrices; α1-matrices; Subdirect sum; Hadamard product

Kategorie tematyczne

• 15A18: Eigenvalues, singular values, and eigenvectors

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 1
• Strony: 32-40

Daty

wydano

2010-02-01

online

2010-02-02

Twórcy

autor

Rafael Bru

• Universitat Politècnica de València

autor

Ljiljana Cvetković

• University of Novi Sad

autor

Vladimir Kostić

• University of Novi Sad

autor

Francisco Pedroche

• Universitat Politècnica de València

Bibliografia

• [1] Berman A., Plemmons R. J., Nonnegative matrices in the mathematical sciences, Academic Press, New York, Revised reprint of the 1979 original, SIAM, Philadelphia, 1994
• [2] Bru R., Pedroche F., Szyld D.B., Subdirect sums of S-Strictly Diagonally Dominant matrices, Electron. J. Linear Algebra, 2006, 15, 201–209
• [3] Cvetkovic L., H-matrix theory vs. eigenvalue localization, Numerical Algorithms, 2006, 42, 229–245 http://dx.doi.org/10.1007/s11075-006-9029-3
• [4] Cvetkovic L., Kostic V., New criteria for identifying H-matrices, J. Comput. Appl. Math., 2005, 180, 265–278 http://dx.doi.org/10.1016/j.cam.2004.10.017
• [5] Elsner L., Mehrmann V., Convergence of block-iterative methods for linear systems arising in the numerical solution of Euler equations, Numer. Math., 1991, 59, 541–560 http://dx.doi.org/10.1007/BF01385795
• [6] Fallat S.M., Johnson C.R., Sub-direct sums and positivity classes of matrices, Linear Algebra Appl., 1999, 288, 149–173 http://dx.doi.org/10.1016/S0024-3795(98)10194-5
• [7] Gan T.B., Huang T.Z., Simple criteria for nonsingular H-matrices, Linear Algebra Appl., 2003, 374, 317–326 http://dx.doi.org/10.1016/S0024-3795(03)00646-3
• [8] Huang T.Z., Leng S.S., Wachspress E.L., Tang Y.Y., Characterization of H-matrices, Computers & Mathematics with applications, 2004, 48(10–11), 1587–1601 http://dx.doi.org/10.1016/j.camwa.2004.04.034
• [9] Ostrowski A.M., Über die Determinanten mit überwiegender Hauptdiagonale, Comentarii Mathematici Helvetici, 1937, 10, 69–96 (in German) http://dx.doi.org/10.1007/BF01214284
• [10] Spiteri P., A new characterization of M-matrices and H-matrices, BIT, 2003, 43, 1019–1032 http://dx.doi.org/10.1023/B:BITN.0000014562.10957.a4
• [11] Varga R.S., Geršgorin and his circles, Springer Series in Computational Mathematics, Vol. 36, Springer, Berlin, Heidelberg, 2004
• [12] Zhu Y., Huang T.Z., Subdirect sums of doubly diagonally dominant matrices, Electron. J. Linear Algebra, 2007, 16, 171–182

Identyfikatory

DOI

10.2478/s11533-009-0068-6