References
- Alvin , K. F. , Peterson , L. D. and Park , K. C. 1995 . Method for determining minimum-order mass and stiffness matrices from modal test data . AIAA J. , 33 ( 1 ) : 128 – 135 .
- Baksalary , J. K. 1984 . Nonnegative definite and positive definite solutions to the matrix equation . Linear Multilinear Alg. , 16 : 133 – 139 .
- Berman , A. 1979 . Mass matrix correction using an incomplete set of measured modes . AIAA J. , 17 ( 10 ) : 1147 – 1148 .
- Chang , X. W. and Wang , J. S. 1993 . The symmetric solution of the matrix equations , and . Linear Alg. Appl. , 179 : 171 – 189 .
- Chu , K. E. 1987 . Singular value and generalized singular value decompositions and the solution of linear matrix equations . Linear Alg. Appl. , 88/89 : 83 – 98 .
- Chu , D. and De Moor , B. 2000 . On a variational formulation of the QSVD and the RSVD . Linear Alg. Appl. , 311 : 61 – 78 .
- Dai , H. and Lancaster , P. 1996 . Linear matrix equations from an inverse problem of vibration theory . Linear Alg. Appl. , 246 : 31 – 47 .
- Deng , Y. B. The solvability conditions for the positive semi-definite solution and positive definite solution of the linear matrix equation . Proceedings of the Seventh China-Japan Seminar on Numerical Mathematics . Edited by: Shi , Z.-C. and Okamoto , H. pp. 203 – 220 . Beijing : Science Press .
- Golub , G. H. and Van Loan , C. F. 1989 . Matrix Computations , 2 , Baltimore : Johns Hopkins University Press .
- Golub , G. H. and Zha , H. 1994 . A perturbation analysis of the canonical correlations of matrix pairs . Linear Alg. Appl. , 210 : 3 – 28 .
- Groß , J. 2000 . Nonnegative-definite and positive-definite solutions to the matrix equation – revisited . Linear Alg. Appl. , 321 : 123 – 129 .
- Higham , N. 1988 . The symmetric Procrustes problem . BIT , 28 : 133 – 143 .
- Horn , R. A. and Johnson , C. R. 1985 . Matrix Analysis , Cambridge : Cambridge University Press .
- Khatri , C. G. and Mitra , S. K. 1976 . Hermitian and nonnegative definite solutions of linear matrix equations . Amer. J. Appl. Math. , 31 : 579 – 586 .
- Lus , H. , De Angelis , M. and Betti , R. 2003 . A new approach for reduced order modeling of mechanical systems using vibration measurements . J. Appl. Mech. (Trans. ASME) , 70 : 715 – 723 .
- Naylor , A. W. and Sell , G. R. 1982 . Linear Operator Theory in Engineering and Science , New York : Springer-Verlag .
- Paige , C. and Saunders , M. 1981 . Towards a generalized singular value decomposition . SIAM J. Numer. Anal. , 18 : 398 – 405 .
- Sun , J. G. 1987 . The least-squares solution of a kind of inverse eigenvalue problems . Math. Numer. Sinica , 2 : 206 – 216 . (in Chinese)
- Xie , D. X. and Zhang , L. 2003 . Least-squares solutions of over positive semidefinite matrices A . J. Comput. Math. , 21 ( 2 ) : 167 – 174 .
- Young , D. M. , Seaman , J. W. and Meaux , L. M. 1999 . Independence distribution preserving covariance structures for the multivariate model . J. Multivariate Anal. , 68 : 165 – 175 .