Least squares solution of BXAT = T over symmetric, skew-symmetric, and positive semidefinite X

SIAM Journal on Matrix Analysis and Applications

Volumn 25, Issue 2, 2004, Pages 486-494

  Deng, Yuan Bei ^a   Hu, X Y ^a   Zhang, Lei ^a  

^a HUNAN UNIVERSITY   (China)

Author keywords

Hadamard product; Least squares problem; Matrix equation; QSVD factorization

Indexed keywords

EID: 1842865576     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479802402491     Document Type: Article

References (24)

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. 537-566.
2. J. C. ALLWRIGHT AND K. G. WOODGATE, Erratum and addendum: "Positive semidefinite matrices: Characterization via conical and least-squares solution of a matrix equation," SIAM J. Control Optim., 28 (1990), pp. 250-251.
3. L.-E. ANDERSSON AND T. ELFVING, A constrained Procrustes problem, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 124-139.
4. A. BEN-ISRAEL AND T. N. E. GREVILLE, Generalized Inverses: Theory and Applications, Wiley, New York, 1974.
5. K.-W. E. CHU, Symmetric solutions of linear matrix equations by matrix decompositions, Linear Algebra Appl., 119 (1989), pp. 35-50.
6. D. CHU AND B. DE MOOR, On a variational formulation of the QSVD and the RSVD, Linear Algebra Appl., 311 (2000), pp. 61-78.
7. F. J. H. DON, On the symmetric solution of a linear matrix equation, Linear Algebra Appl., 93 (1987), pp. 1-7.
8. R. ESCALANTE AND M. RAYDAN, Dykstra's algorithm for a constrained least-squares matrix problem, Numer. Linear Algebra Appl., 3 (1996), pp. 459-472.
9. R. ESCALANTE AND M. RAYDAN, Dykstra's algorithm for constrained least-squares rectangular matrix problems, Comput. Math. Appl., 35 (1998), pp. 73-79.
10. D. W. FAUSETT AND C. T. FULTON, Large least squares problems involving Kronecker products, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 219-227.
11. G. H. GOLUB AND J. H. WELSCH, Calculation of Gauss quadrature rules, Math. Comput., 23 (1969), pp. 221-230.
12. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, Johns Hopkins University Press, Baltimore, MD, 1989.
13. O. HALD, On Discrete and Numerical Sturm-Liouville Problems, Ph.D. dissertation, Department of Mathematics, New York University, New York, 1972.
14. N. J. HIGHAM, Computing a nearest symmetric positive semidefinite matrix, Linear Algebra Appl., 103 (1988), pp. 103-118.
15. N. J. HIGHAM, The symmetric Procrustes problem, BIT, 28 (1988), pp. 133-143.
16. D. HUA, On the symmetric solutions of linear matrix equations, Linear Algebra Appl., 131 (1990), pp. 1-7.
17. D. HUA AND P. LANCASTER, Linear matrix equations from an inverse problem of vibration theory, Linear Algebra Appl., 246 (1996), pp. 31-47.
18. J. R. MAGNUS, L-structured matrices and linear matrix equations, Linear and Multilinear Algebra, 14 (1983), pp. 67-88.
19. J. SUN, Two kinds of inverse eigenvalue problems for real symmetric matrices, Math. Numer. Sinica, 3 (1988), pp. 282-290.
20. K. G. WOODGATE, Least-squares solution of F = PG over positive semidefinite symmetric P, Linear Algebra Appl., 245 (1996), pp. 171-190.
21. D.-X. XIE, Least-squares solution for inverse eigenpair problem of nonnegative definite matrices, Comput. Math. Appl., 40 (2000), pp. 1241-1251.
22. H. Y. ZHA, Comments on "Large least squares problems involving Kronecker products," SIAM J. Matrix Anal. Appl., 16 (1995), p. 1172.
23. L. ZHANG, The approximation on the closed convex cone and its numerical application, Hunan Ann. Math., 6 (1986), pp. 16-22.
24. L. ZHANG, A class of inverse eigenvalue problem for symmetric nonnegative matrices, J. Hunan Educ. Inst., 13 (1995), pp. 11-17.