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Approximation by a Hermitian positive semidefinite Toeplitz matrix. (English) Zbl 0784.15015
The authors study the problem of finding the closest Hermitian positive semidefinite Toeplitz matrix of a given rank to an arbitrary given matrix (in the Frobenius norm = Hilbert-Schmidt norm). They introduce two methods, one is based on using a special orthonormal basis in the space of Hermitian Toeplitz matrices and the second is a modified alternating projection method. Some numerical results associated with their methods are given.
Reviewer: N.M.Zobin (Haifa)

MSC:
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15B48 Positive matrices and their generalizations; cones of matrices
15B57 Hermitian, skew-Hermitian, and related matrices
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