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This paper presents a distributed algorithm for solving a linear algebraic equation of the form Ax = b where A is an n × n nonsingular matrix and b is an n-vector. The equation is solved by a network of n agents assuming that each agent knows exactly one distinct row of the partitioned matrix [A b], the current estimates of the equation's solution generated by its neighbors, and nothing more. Each...
The spectral properties of saddle point matrices arising from saddle point problems are discussed. The relations of the eigenvalues and the determinants between the saddle point matrices and their sub blocks are investigated. An appropriate estimate on the maximum eigenvalue of saddle point matrix is given. In the numerical experiment the saddle point matrices derived from the mixed finite element...
This paper investigates the stability and boundary of a swarm with a general directed and weighted topology. The stability of a swarm is generally considered as cohesiveness. We construct a symmetric eigenmatrix and define an orthogonal eigenparameter which reflects the degree of orthogonality between the left eigenvector of the coupling matrix corresponding to its zero eigenvalue and the eigenvectors...
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