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The problem of finding the eigenvector corresponding to the largest eigenvalue of a stochastic matrix has numerous applications in ranking search results, multi-agent consensus, networked control and data mining. The well-known power method is a typical tool for its solution. However randomized methods could be competitors vs standard ones; they require much less calculations for one iteration and...
In this paper, we study the Hermitian positive definite solutions of the nonlinear matrix equation X + A* X-2 A = I . Suppose X is a Hermitian positive definite solution of this equation. We discuss the relation between X and A by the eigenvalue and eigenvector of X and A respectively.
Recently spectral clustering has become one of the most popular clustering algorithms. Although it has many advantages, it still has a lot of shortcomings which should be resolved, such as there are a wide variety of spectral clustering algorithms that use the eigenvectors in slightly different ways and many of these algorithms have no proof that they will actually compute a reasonable clustering...
In this paper we propose a general approach for determining classes of n-th order digital filters with two's complement overflow which have invariant subspaces and analytically determine their positions and/or their boundaries. The proposed approach is based on analysis of projections of trajectories on adequately chosen directions in the filter phase space.
In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X + A* X-2 A = I are studied. We discuss the relation between X and A by the eigenvalue and eigenvector of X and A respectively, and the property of numerical range of A . An iterative method for obtaining positive definite solutions of the equation is constructed.
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