A constrained procrustes problem

SIAM Journal on Matrix Analysis and Applications

Volumn 18, Issue 1, 1997, Pages 124-139

  Andersson, Lars Erik ^a   Elfving, Tommy ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Constrained matrices; Convex cones; Positive semidefinite; Procrustes

Indexed keywords

EID: 0031539943     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479894277545     Document Type: Article

References (29)

1. J. C. ALLWRIGHT. Positive semidefinite matrices: Characterization via conical hulls and least-squares solution of a matrix equation, SIAM J. Control Optim., 26 (1988), pp. 537-556.
2. C. A. BEATTIE AND S. W. SMITH, Optimal matrix approximants in structural identification, J. Optim. Theory Appl., 74 (1992), pp. 23-56.
3. A. BERMAN AND R. J. PLEMMONS, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.
4. D. P. BERTSEKAS AND J. N. TSITSIKLIS, Parallel and Distributed Computing, Prentice-Hall, Englewood Cliffs, NJ, 1989.
5. A. BJÖRCK, A direct method for sparse least squares problems with lower and upper bounds, Numer. Math., 54 (1988), pp. 19-32.
6. A. BJÖRCK, Numerical Methods for Least Squares Problems, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1996.
7. J. E. BROCK, Optimal matrices describing linear systems, AIAA J., 6 (1968), pp. 1292-1296.
8. M. T. CHU AND K. R. DRIESSEL, The projected gradient method for least squares matrix approximations with spectral constraints, SIAM J. Numer. Anal., 27 (1990), pp. 1050-1060.
9. K. FAN AND A. J. HOFFMAN. Some matrix inequalities in the space of matrices, Proc. Amer. Math. Soc., 6 (1955), pp 111-116.
10. R. FLETCHER, Practical Methods of Optimization, 2nd edition, Wiley, New York, 1987.
11. A. FRIEDLANDER AND J. M. MARTINEZ, On the maximization of a concave quadratic function with boxconstraints, SIAM J. Optim., 4 (1994), pp. 177-192.
12. M. S. GOWDA, Minimising quadratic functional over closed convex cones, Bull. Austral. Math. Soc., 39 (1989), pp. 15-20.
13. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 2nd edition, The Johns Hopkins University Press, London, 1989.
14. M. HALL JR., Combinatorial Theory, 2nd edition, Wiley, New York, 1986.
15. P. HALMOS, Positive approximants of operators, Indiana Univ. Math. J., 21 (1972), pp. 951-960.
16. S.-P. HAN, A successive projection method, Math. Programming, 40 (1988), pp. 1-14.
17. S.-P. HAN AND G. LOU, A parallel algorithm for a class of convex programs, SIAM J. Control Optim., 26 (1988), pp. 345-355.
18. N. J. HIGHAM, The symmetric Procrustes problem, BIT, 28 (1988), pp. 133-143.
19. N. J. HIGHAM, Computing a nearest symmetric positive semidefinite matrix, Linear Algebra Appl., 103 (1988), pp. 103-118.
20. E. ISAACSON AND H. B. KELLER, Analysis of Numerical Methods, Wiley, New York, 1966.
21. A. N. IUSEM AND A. R. DE PIERRO, On the convergence of Han's method for convex programming with quadratic objective, Math. Programming, 52 (1991), pp. 265-284.
22. D. G. LUENBERGER, Linear and Nonlinear Programming, 2nd ed., Addison-Wesley, Reading, MA, 1984.
23. Z.-Q. LUO AND P. TSENG, On the linear convergence of descent methods for convex essentially smooth minimization, SIAM J. Control Optim., 30 (1992), pp. 408-425.
24. R. T. ROCKAFELLAR, Convex analysis, Princeton University Press, Princeton, NJ, 1970.
25. A. RUHE, Closest normal matrix finally found!, BIT, 27 (1987), pp. 585-598.
26. J. STOER AND C. WITZGALL, Convexity and Optimization in Finite. Dimensions I, Springer-Verlag, New York, 1970.
27. G. STRANG, Introduction to Applied Mathematics, Wellesley-Cambridge Press, Wellesley, MA, 1986.
28. T. J. SUFFRIDGE AND T. L. HAYDEN, Approximation by a Hermitian positive semidefinite Toeplitz matrix, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 721-734.
29. K. G. WOODGATE, Least-Squares Solution of F = PG over Positive Semi-Definite Symmetric P*, Technical Report, Dept. of Aeronautics, Imperial College of Science, Technology and Medicine, London, January 1993.