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Positive definite constrained least-squares estimation of matrices. (English) Zbl 0847.65024

The problem of finding a symmetric matrix \(X\) minimizing \(B-XA\) in the least squares sense, under the condition that all eigenvalues of \(X\) exceed a given positive value, is solved by means of a sequence of quadratic programming problems. A suboptimal variant, which is guaranteed to converge in a finite number of \(QP\) steps, is given as an alternative to the optimal algorithm, which may approach a solution asymptotically.
Reviewer: A.Ruhe (Göteborg)

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
65K05 Numerical mathematical programming methods
90C20 Quadratic programming
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