Best approximate solution of matrix equation AXB + CYD = E

SIAM Journal on Matrix Analysis and Applications

Volumn 27, Issue 3, 2005, Pages 675-688

  Liao, A N Ping ^a   Bai, Zhong Zhi ^b,c   Lei, Yuan ^a  

^a HUNAN UNIVERSITY   (China)

^b FUDAN UNIVERSITY   (China)

^c CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Best approximate solution; Canonical correlation decomposition; Generalized singular value decomposition; Least squares solution; Matrix equation

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; LEAST SQUARES APPROXIMATIONS; LINEAR EQUATIONS; PROBLEM SOLVING; THEOREM PROVING;

BEST APPROXIMATE SOLUTION; CANONICAL CORRELATION DECOMPOSITION; GENERALIZED SINGULAR VALUE DECOMPOSITION; LEAST-SQUARES SOLUTION; MATRIX EQUATION;

MATRIX ALGEBRA;

EID: 33746145952     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/040615791     Document Type: Article

References (30)

1. J. K. BAKSALAKY AND R. KALA, The matrix equation AXB+CYD = E, Linear Algebra Appl., 30 (1980), pp. 141-147.
2. M. BARUCH, Optimisation procedures to correct stiffness and flexibility matrices using vibration data, AIAA J., 16 (1978), pp. 1208-1210.
3. M. BARUOH AND I. Y. BAR-ITZACK, Optimal weighted orthogonalization of measured modes, AIAA J., 16 (1978), pp. 346-351.
4. K. E. CHU, Singular value and generalized singular value decomposition and the solution of linear matrix equations, Linear Algebra Appl., 88/89 (1987), pp. 83-98.
5. B. N. DATTA, finite element model updating, eigenstructure assignment, and eigenvalue embedding techniques for vibrating systems, Mech. Syst. Signal Process., 16 (2002), pp. 83-96.
6. M. I. FRISWELL, D. J. INMAN, AND D. F. PILKEY, Direct updating of damping and stiffness matrices, AIAA J., 36 (1998), pp. 491-193.
7. M. I. FRISWELL AND J. E. MOTTERSHEAD, Finite Element Model Updating in Structural Dynamics, Kluwer Academic Publishers B, Dordrecht, Boston, London, 1995.
8. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 3rd ed., The Johns Hopkins University Press, Baltimore, London, 1996.
9. G. H. GOLUB AND H. ZHA, Perturbation analysis of the canonical correlations of matrix pairs, Linear Algebra Appl., 210 (1994), pp. 3-28.
10. N. J. HIGHAM, Computing a nearest symmetric positive semidefinte matrix, Linear Algebra Appl., 103 (1988), pp. 103-118.
11. R. J. HORN AND C. R. JOHNSON, Topics in Matrix Analysis, Cambridge University Press, Cambridge, UK, 1991.
12. L.-P. HUANG AND Q.-G. ZENO, The matrix equation AXB + CYD = E over a simple Artinian ring, Linear and Multilinear Algebra, 38 (1996), pp. 226-232.
13. D. J. INMAN AND J. DANIEL, Vibration with Control, Measurement, and Stability, Prentice-Hall, Englewood Cliffs, NJ, 1989.
14. Z.-X. JIANG AND Q.-S. LU, On optimal approximation of a matrix under spectral restriction, Math. Numer. Sinica, 8 (1986), pp. 47-62 (In Chinese).
15. A.-P. LIAO AND Z.-Z. BAI, The constrained solutions of two matrix equations, Acta Math. Sinica (Engl. Ser.), 18 (2002), pp. 671-678.
16. A.-P. LIAO AND Z.-Z. BAI, Least-squares solutions of the matrix equation A*XA = D in bisymmetric matrix sci, Math. Numer. Sinica, 24 (2002), pp. 9-20 (in Chinese).
17. A.-P. LIAO AND Z.-Z. BAI, Least-squares solution of AXB = D over Symmetric positive semidefinite matrices X, J. Comput. Math., 21 (2003), pp. 176-182.
18. T = C with the least norm, Math. Numer. Sinica, 27 (2006), pp. 81-96 (in Chinese).
19. C. C. PAIGB AND M. A. SAUNDERS, Towards a generalized singular value decomposition, SIAM J. Numer. Anal., 18 (1981), pp. 398-406.
20. R. PENROSE, On best approximate solutions of linear matrix equations, Proc. Cambridge Philos. Soc., 62 (1966), pp. 17-19.
21. W. E. ROTH, The equations AX - YB - C and AX - XB = C in matrices, Proc. Amer. Math. Soc., 3 (1962), pp. 392-396.
22. G. W. STEWART, Computing the CS-decomposition of a partitioned orthogonal matrix, Numer. Math, 40 (1982), pp. 297-306.
23. G. W. STEWART AND J.-Q. SUN, Matrix Perturbation Theory, Academic Press, New York, 1990.
24. S.-Y. SHIM AND Y. CHEN, Least squares solution of matrix equation AXB* + CYD* = E, SIAM J. Matrix Anal. Appl., 24 (2003), pp. 802-808.
25. A. B. ÖZOÜLER, The equation AXB + CYD = E over a principal ideal domain, SIAM J. Matrix Anal. Appl., 12 (1991), pp. 681-691.
26. R.-S. WANG, Functional Analysis and Optimization Theory, Beijing University of Aeronautics and Astronautici Press, Beijing, 2003 (In Chinese).
27. G.-P. XU, M.-S. WBI, AND D.-S. ZHENG, On solutions of matrix equation AXB + CYD = F, Linear Algebra Appl., 279 (1998), pp. 93-109.
28. Y.-X. YUAN, The minimum norm solutions of two classes of matrix equations, Numer. Math. J. Chinese Univ., 24 (2002), pp. 127-134 (In Chinese).
29. Y.-X. YUAN, The optimal solution of linear matrix equation by using matrix decompositions, Math. Numer. Sinica, 24 (2002), pp. 166-176 (in Chinese).
30. L. ZHANG, Approximation on a closed convex cone and its numerical application, Hunan Ann. Math., 6 (1986), pp. 16-22 (in Chinese).