81 research outputs found
More on minors of Hermitian (quasi-)Laplacian matrix of the second kind for mixed graphs
A mixed graph is the graph obtained from an unoriented simple graph
by giving directions to some edges of , where is often called the
underlying graph of . In this paper, we introduce two classes of
incidence matrices of the second kind of , and discuss the determinants
of these two matrices for rootless mixed trees and unicyclic mixed graphs.
Applying these results, we characterize the explicit expressions of various
minors for Hermitian (quasi-)Laplacian matrix of the second kind of .
Moreover, we give two sufficient conditions that the absolute values of all the
cofactors of Hermitian (quasi-)Laplacian matrix of the second kind are equal to
the number of spanning trees of the underlying graph .Comment: 16 pages,7 figure
Convergence of generalized AOR iterative method for linear systems with strictly diagonally dominant matrices
AbstractIn this paper, some improvements on Darvishi and Hessari [On convergence of the generalized AOR method for linear systems with diagonally dominant coefficient matrices, Appl. Math. Comput. 176 (2006) 128β133] are presented for bounds of the spectral radius of lΟ,r, which is the iterative matrix of the generalized AOR (GAOR) method. Subsequently, some new sufficient conditions for convergence of GAOR method will be given, which improve some results of Darvishi and Hessari [On convergence of the generalized AOR method for linear systems with diagonally dominant coefficient matrices, Appl. Math. Comput. 176 (2006) 128β133]
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