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The sufficient conditions for determining the non-singular H-matrices were given by applying the theory of diagonally dominant matrix. Then, the results of a recent study were promoted and improved with such conditions. Through the analysis of a numerical example, the proposed conditions were proved as more applicable than those in the reference.
Non-singular H-matrix, Diagonal dominance, Irreducibility, Chain of nonzero elements.
1. Q. Tuo, L. Zhu, J.Z. Liu, New determination conditions for non-singular H-matrices, 2008, Journal of Computational Mathematics, vol. 30, pp. 177-182.
2. R.S. Varga, On recurring theorems on diagonal dominance, 1976, Linear Algebra Appl., vol. 13, pp. 1-9.
3. M.X. Pang, Determinants and applications of generalized diagonally dominant matrices, 1985, Chinese Annals of Mathematics, vol. 6A, no. 3, pp. 323-330.
A. Berman, R.J. Plemmons, Nonnegative matrices in the mathematical sciences, 1994, SIAM Press, Philadelphia, pp. 773-736.
4. Y.X. Sun, Improvement on a theorem by Ostrowski and its Applications, 1991, Northeast Math., vol. 7, no. 4, pp. 497-502.
5. S.X. Tian, Criteria conditions for generalized diagonally dominant matrices, 2007, Chinese Quarterly Journal of Mathematrucs, vol. 22, no. 1, pp. 63-67.
6. R.A. Brualdi, Regions in the complex plane containing the eigenvalues of a matrix, 1994, Amer. Math. Monthly, vol. 101, pp. 975-985.
7. R.A. Horn, C.R. Johnson, Matrix Analysis, 1885, Cambridge University Press, New York.
8. J.Z. Liu, A.Q. He, A parallel characterization of H-matrices, 2009, International Journal Computer Math, vol. 86, no. 7, pp.1160-1166.
9. T.B. Gan, Simple Criteria for Nonsingular H-matrix, 2003, Linear Algebra Apply, no. 374, pp. 317-326.