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This paper presents a parallel refined Jacobi-Davidson method for computing extreme eigenpairs of quadratic eigenvalue problems. The method directly computes the refined Ritz pairs in the projection subspace, and expands the subspace by the solution of the correction equation. Combining with the restarting scheme, the method can solve several eigenpairs of quadratic eigenvalue problems. The numerical...
In this paper, we present dynamical systems for computing the low rank approximation of a single matrix and of a set of matrices. These dynamical systems arise from solving an optimization problem involving these matrices. The proposed methods are based on applying smooth optimization techniques on smooth manifolds. Many of these systems are then modified to obtain power-like methods for computing...
In this paper, the solvability conditions and the general solution of matrix equations (AX=B,XC=D) with a submatrix constraint are obtained by using the SVD(singular value decomposition) of matrix. In addition, the expression of the optimal approximation solution to a given matrix is derived.
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