Perturbation analysis of the matrix sign function

Linear Algebra and Its Applications

Volumn 250, Issue , 1997, Pages 177-206

  Sun, Ji Guang ^a  

^a UMEÅ UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031537607     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/0024-3795(95)00522-6     Document Type: Article

References (18)

1. Z. Bai and J. Demmel, Design of a Parallel Nonsymmetric Eigenroutine Toolbox, Part II, Technical Report, Dept. of Mathematics, Univ. of California, Berkeley, 1994.
2. L. A. Balzer, Accelerated convergence of the matrix sign function method of solving Lyapunov, Riccati and other matrix equations, Internat. J. Control 32:1057-1078 (1980).
3. A. N. Beavers, Jr., and E. D. Denman, A computational method for eigenvalues and eigenvectors of a matrix with real eigenvalues, Numer. Math. 21:389-396 (1973).
4. R. Byers, A bisection method for measuring the distance of a stable matrix to the unstable matrices, SIAM J. Sci. Statist. Comput. 9:875-881 (1988).
5. R. Byers, C. He, and V. Mehrmann, The matrix sign function method and the computation of invariant subspaces, manuscript, Sept. 1994.
6. G. Golub and C. Van Loan, Matrix Computations, 2nd ed., Johns Hopkins U.P., Baltimore, 1989.
7. N. J. Higham, The matrix sign decomposition and its relation to the polar decomposition, Linear Algebra Appl. 212/213:3-20 (1994).
8. D. Hinrichsen and A. J. Pritchard, Stability radius for structured perturbations and the algebraic Riccati equation, Systems Control Lett. 8:105-113 (1986).
9. C. Kenney and A. J. Laub, Polar decomposition and matrix sign function condition estimates, SIAM J. Sci. Statist. Comput. 12:488-504 (1991).
10. C. Kenney and A. J. Laub, The Matrix Sign Function, Technical Report, Univ. of California, Santa Barbara, 1994.
11. P. Lancaster and M. Tismenetsky, The Theory of Matrices, 2nd ed., Academic, New York, (1985).
12. R. Mathias, Condition estimation for matrix function via the Schur decomposition, SIAM J. Matrix Anal. Appl., to appear.
13. J. D. Roberts, Linear model reduction and solution of the algebraic Riccati equation, Internat. J. Control 32:677-687 (1980); also Technical Report, Univ. of Cambridge, 1971.
14. G. W. Stewart, Error and perturbation bounds for subspaces associated with certain eigenvalue problems, SIAM Rev. 15:727-764 (1973).
15. G. W. Steward and J.-G. Sun, Matrix Perturbation Theory, Academic, Boston, 1990.
16. J.-G. Sun, Estimation of the separation of two matrices, J. Comput. Math. 2:189-200 (1984).
17. J.-G. Sun, Perturbation expansion for invariant subspaces, Linear Algebra Appl. 153:85-97 (1991).
18. C. F. Van Loan, How near is a stable matrix to an unstable matrix? Contemp. Math. 47:465-477 (1985).