On graph compatible splittings of M-matrices. (English) Zbl 0621.65023
The author supplies families of examples that answer negatively the following question posed by H. Schneider [ibid. 58, 407-424 (1984; Zbl 0561.65020)]. Let A and M be M-matrices, \(M^{-1}\geq 0\), \(A=M-N\), \(N\geq 0\). Does the reflexive and transitive closure of the graph of A contain the graph of M ?
Reviewer: D.Powers
MSC:
| 65F10 | Iterative numerical methods for linear systems |
| 15A06 | Linear equations (linear algebraic aspects) |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
Citations:
Zbl 0561.65020References:
| [1] | Berman, A.; Plemmons, R., Non-negative Matrices in the Mathematical Sciences (1979), Academic: Academic New York · Zbl 0484.15016 |
| [2] | Schneider, H., Theorems on \(M\)-splittings of a singular \(M\)-matrix which depend on graph structure, Linear Algebra Appl., 58, 407-429 (1984) · Zbl 0561.65020 |
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