In this paper, the σ_duals of two classes important sequence spaces l 1(X) and l ∞(X) are investigated, and shows that some topology properties of locally convex space (X,τ) can be characterized by the σ _dua...In this paper, the σ_duals of two classes important sequence spaces l 1(X) and l ∞(X) are investigated, and shows that some topology properties of locally convex space (X,τ) can be characterized by the σ _duals. The criterions of bounded sets in l 1(X) and l ∞(X ) with respect to the weak topologies generated by the σ _duals are obtained. Furthermore, a Schur type result and an automatic continuity theorem of matrix transformation are established.展开更多
The matrix rank minimization problem arises in many engineering applications. As this problem is NP-hard, a nonconvex relaxation of matrix rank minimization, called the Schatten-p quasi-norm minimization(0 < p <...The matrix rank minimization problem arises in many engineering applications. As this problem is NP-hard, a nonconvex relaxation of matrix rank minimization, called the Schatten-p quasi-norm minimization(0 < p < 1), has been developed to approximate the rank function closely. We study the performance of projected gradient descent algorithm for solving the Schatten-p quasi-norm minimization(0 < p < 1) problem.Based on the matrix restricted isometry property(M-RIP), we give the convergence guarantee and error bound for this algorithm and show that the algorithm is robust to noise with an exponential convergence rate.展开更多
Estimate bounds for the Perron root of a nonnegative matrix are important in theory of nonnegative matrices.It is more practical when the bounds are expressed as an easily calcu-lated function in elements of matrices....Estimate bounds for the Perron root of a nonnegative matrix are important in theory of nonnegative matrices.It is more practical when the bounds are expressed as an easily calcu-lated function in elements of matrices.For the Perron root of nonnegative irreducible matrices,three sequences of lower bounds are presented by means of constructing shifted matrices,whose convergence is studied.The comparisons of the sequences with known ones are supplemented with a numerical example.展开更多
文摘In this paper, the σ_duals of two classes important sequence spaces l 1(X) and l ∞(X) are investigated, and shows that some topology properties of locally convex space (X,τ) can be characterized by the σ _duals. The criterions of bounded sets in l 1(X) and l ∞(X ) with respect to the weak topologies generated by the σ _duals are obtained. Furthermore, a Schur type result and an automatic continuity theorem of matrix transformation are established.
基金supported by National Natural Science Foundation of China(Grant No.11171299)
文摘The matrix rank minimization problem arises in many engineering applications. As this problem is NP-hard, a nonconvex relaxation of matrix rank minimization, called the Schatten-p quasi-norm minimization(0 < p < 1), has been developed to approximate the rank function closely. We study the performance of projected gradient descent algorithm for solving the Schatten-p quasi-norm minimization(0 < p < 1) problem.Based on the matrix restricted isometry property(M-RIP), we give the convergence guarantee and error bound for this algorithm and show that the algorithm is robust to noise with an exponential convergence rate.
基金the National Natural Science Foundation of China (No.10771030)Project for Academic Leader and Group of UESTC (No.L08011001JX0776)
文摘Estimate bounds for the Perron root of a nonnegative matrix are important in theory of nonnegative matrices.It is more practical when the bounds are expressed as an easily calcu-lated function in elements of matrices.For the Perron root of nonnegative irreducible matrices,three sequences of lower bounds are presented by means of constructing shifted matrices,whose convergence is studied.The comparisons of the sequences with known ones are supplemented with a numerical example.
