Criteria for generalized diagonally dominant matrices and \(M\)-matrices. (English) Zbl 0757.15010
Necessary and sufficient conditions are developed for identifying generalized diagonally dominant matrices. These are utilized for developing some criteria for judging nonsingular \(M\)-matrices. Some numerical examples are worked out for illustrating these criteria.
Reviewer: J.K.Sengupta (Santa Barbara)
MSC:
| 15B48 | Positive matrices and their generalizations; cones of matrices |
| 65F10 | Iterative numerical methods for linear systems |
References:
| [1] | Taussky, O., A recurring theorem on determinants, Amer. Math. Monthly, 56, 672-676 (1949) · Zbl 0036.01301 |
| [2] | Schivakumar, P. N.; Chew, K. H., A sufficient condition for nonvanishing of determinants, Proc. Amer. Math. Soc., 43, 63-66 (1974) · Zbl 0262.15008 |
| [3] | Gao, Yi-ming, Criteria of the generalized diagonally dominant and nonsingular matrices, Northeast Normal Univ., 3, 23-28 (1982) · Zbl 0566.15003 |
| [4] | Gao, Yi-ming, Criteria of the generalized diagonally dominant and nonsingular matrices (II), J. Eng. Math., 5, 12-17 (1988) |
| [5] | Berman, A.; Plemmons, R. J., Nonnegative Matrices in the Mathematical Sciences (1979), Academic: Academic New York · Zbl 0484.15016 |
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