Node importance or centrality evaluation is an important methodology for network analysis.In this paper,we are interested in the study of objects appearing in several networks.Such common objects are important in network-network interactions via object-object interactions.The main contribution of this paper is to model multiple networks where there are some common objects in a multivariate Markov chain framework,and to develop a method for solving common and non-common objects’stationary probability distributions in the networks.The stationary probability distributions can be used to evaluate the importance of common and non-common objects via network-network interactions.Our experimental results based on examples of co-authorship of researchers in different conferences and paper citations in different categories have shown that the proposed model can provide useful information for researcher-researcher interactions in networks of different conferences and for paperpaper interactions in networks of different categories.
In this paper, we consider preconditioners for generalized saddle point systems with a nonsymmetric coefficient matrix. A constraint preconditioner for this systems is constructed, and some spectral properties of the preconditioned matrix are given. Our results extend the corresponding ones in [3] and [4].
CHEN Xiao-shan LI Wen School of Mathematics, South China Normal University, Guangzhou 510631, China
A complex,square matrix E is called coninvolutory if E = I,where denotes complex conjugate of the matrix E and I is an identity matrix.In this paper we introduce the coninvolutory decomposition of a complex matrix and investigate a Newton iteration for computing the coninvolutory factor.A simple numerical example illustrates our results.
