Hu, H. Positive definite constrained least-squares estimation of matrices. (English) Zbl 0847.65024 Linear Algebra Appl. 229, 167-174 (1995). 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) Cited in 6 Documents MSC: 65F20 Numerical solutions to overdetermined systems, pseudoinverses 65K05 Numerical mathematical programming methods 90C20 Quadratic programming Keywords:least squares estimation; quadratic programming PDFBibTeX XMLCite \textit{H. Hu}, Linear Algebra Appl. 229, 167--174 (1995; Zbl 0847.65024) Full Text: DOI References: [1] Allwright, J. C., Positive semidefinite matrices: Characterization via conical hulls and least-squares solution of a matrix equation, SIAM J. Control Optim., 26, 537-555 (1988) · Zbl 0643.65020 [2] Dantzig, G. B., Deriving a Utility Function for the Economy, (Technical Report, SOL 85-6R (1985), Dept. of Operations Research, Stanford Univ) · Zbl 0125.09607 [3] Fletcher, R., A nonlinear programming problem in statistics (educational testing), SIAM J. Sci. Statist. Comput., 2, 257-267 (1981) · Zbl 0475.62089 [4] Fletcher, R., Semi-definite matrix constraints in optimization, SIAM J. Control Optim., 23, 493-513 (1985) · Zbl 0567.90088 [5] Geromel, J. C., On the determination of a diagonal solution of the Lyapunov equation, IEEE Trans. Automat. Control, AC-30, 404-406 (1985) · Zbl 0589.65033 [6] Gill, P. E.; Murray, W.; Saunders, M. A.; Wright, M. H., User’s Guide for LSSOL (1986), Dept. of Operations Research, Stanford Univ, SOL 86-1 [7] Hu, H.; Olkin, I., Finding the positive definite matrix closest to a patterned matrix, Statist. Probab. Lett., 12, 511-515 (1991) · Zbl 0850.62486 [8] Johnson, C. R., Matrix completion problem: A survey, (Proc. Sympos. Appl. Math., 40 (1990)), 171-198 [9] Mayne, D. Q.; Sahba, M., An efficient algorithm for solving inequalities, J. Optim. Theory Appl., 45, 407-423 (1985) · Zbl 0543.65043 [10] Smith, B. T.; Boyle, J. M.; Klema, V. C.; Moler, C. B., Matrix Eigensystems Routines Guide (1970), Springer-Verlag: Springer-Verlag Berlin · Zbl 0289.65017 [11] Zangwill, W. I., Nonlinear programming: A unified approach (1969), Prentice-Hall · Zbl 0191.49101 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.