New Practical Determination of Non-Singular H-Matrices

New Practical Determination of Non-Singular H-Matrices

Chunyu YangShuping Pan 

Public Mathematics, School of Science, Jilin Institute of Chemical Technology, Jilin 132022, China

Corresponding Author Email:
10 June 2017
29 June 2017
30 June 2017
| Citation



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. Introduction
2. Analysis
3. Numerical Example
4. Annex

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.