Theorems on M-Splittings of a Singular M-Matrlx Which Depend on Graph Structure·
نویسندگان
چکیده
Let A = M N E IR nn be a splitting. We investigate the spectral properties of the iteration matrix M 1 N by considering the relationships of the graphs of A, M, N, and M1 N. We call a splitting an M-splitting if M is a nonsingular M-matrix and N;;. O. For an M-splitting of an irreducible Z-matrix A we prove that the circuit index of M1 N is the greatest common divisor of certain sets of integers associated with the circuits of A. For M-splittings of a reducible singular M-matrix we show that the spectral radius of the iteration matrix is 1 and that its multiplicity and index are independent of the splitting. These results hold under somewhat weaker assumptions.
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