# Characterization of α1 and α2-matrices

Rafael Bru; Ljiljana Cvetković; Vladimir Kostić; Francisco Pedroche

Open Mathematics (2010)

- Volume: 8, Issue: 1, page 32-40
- ISSN: 2391-5455

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topRafael Bru, et al. "Characterization of α1 and α2-matrices." Open Mathematics 8.1 (2010): 32-40. <http://eudml.org/doc/268975>.

@article{RafaelBru2010,

abstract = {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.},

author = {Rafael Bru, Ljiljana Cvetković, Vladimir Kostić, Francisco Pedroche},

journal = {Open Mathematics},

keywords = {H-matrices; α1-matrices; Subdirect sum; Hadamard product; -matrices; -matrices; subdirect sum},

language = {eng},

number = {1},

pages = {32-40},

title = {Characterization of α1 and α2-matrices},

url = {http://eudml.org/doc/268975},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Rafael Bru

AU - Ljiljana Cvetković

AU - Vladimir Kostić

AU - Francisco Pedroche

TI - Characterization of α1 and α2-matrices

JO - Open Mathematics

PY - 2010

VL - 8

IS - 1

SP - 32

EP - 40

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/268975

ER -

## References

top- [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 Zbl0815.15016
- [2] Bru R., Pedroche F., Szyld D.B., Subdirect sums of S-Strictly Diagonally Dominant matrices, Electron. J. Linear Algebra, 2006, 15, 201–209 Zbl1142.15307
- [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 Zbl1107.15012
- [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 Zbl1073.65038
- [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 Zbl0744.65026
- [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 Zbl0973.15013
- [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 Zbl1033.15019
- [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 Zbl63.0035.01
- [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 Zbl1053.65022
- [11] Varga R.S., Geršgorin and his circles, Springer Series in Computational Mathematics, Vol. 36, Springer, Berlin, Heidelberg, 2004 Zbl1057.15023
- [12] Zhu Y., Huang T.Z., Subdirect sums of doubly diagonally dominant matrices, Electron. J. Linear Algebra, 2007, 16, 171–182 Zbl1151.15025