Nonsmooth Matrix Valued Functions Defined by Singular Values
نویسندگان
چکیده
A class of matrix valued functions defined by singular values of nonsymmetric matrices are shown to have many properties analogous to matrix valued functions defined by eigenvalues of symmetric matrices. In particular, the (smoothed) matrix valued Fischer-Burmeister function is proved to be strongly semismooth everywhere. This result is also used to show the strong semismoothness of the (smoothed) vector valued Fischer-Burmeister function associated with the second order cone. The strong semismoothness of singular values of a nonsymmetric matrix is discussed and used to analyze the quadratic convergence of Newton’s method for solving the inverse singular value problem.
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