Numerical solution of generalized Lyapunov equations

Advances in Computational Mathematics

Volumn 8, Issue 1-2, 1998, Pages 33-48

  Penzl, Thilo ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Condition estimation; Generalized Lyapunov equation; Generalized Stein equation; Mathematical software

Indexed keywords

EID: 0032342953     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018979826766     Document Type: Article

References (19)

1. E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov and D. Sorenson, LAPACK Users' Guide (SIAM, Philadelphia, PA, 1992).
2. R.H. Bartels and G.W. Stewart, Solution of the equation AX + XB = C, Comm. ACM 15 (1972) 820-826.
3. T = C, IEEE Trans. Automat. Control 29 (1984) 926-928.
4. K.-W.E. Chu, The solution of the matrix equation AXB - CXD = Y and (YA-DZ, YC-BZ) = (E, F), Linear Algebra Appl. 93 (1987) 93-105.
5. J.J. Dongarra, J.R. Bunch, C.B. Moler and G.W. Stewart, UNPACK Users' Guide (SIAM, Philadelphia, PA, 1979).
6. B.S. Garbow, J.M. Boyle, J.J. Dongarra and C.B. Moler, Matrix Eigensystem Routines - EISPACK Guide Extension, Lecture Notes in Computer Science 51 (Springer, New York, 1977).
7. T = E, ACM Trans. Math. Software 18 (1992) 223-231.
8. T = E, ACM Trans. Math. Software 18 (1992) 232-238.
9. G.H. Golub and C.F. Van Loan, Matrix Computations (Johns Hopkins University Press, Baltimore, MD, 3rd ed., 1996).
10. W.W. Hager, Condition estimates, SIAM J. Sci. Statist. Comput 5 (1984) 311-316.
11. S.J. Hammarling, Numerical solution of the stable, non-negative definite Lyapunov equation, IMA J. Numer. Anal. 2 (1982) 303-323.
12. S.J. Hammarling, Numerical solution of the discrete-time, convergent, non-negative definite Lyapunov equation, Systems Control Lett. 17 (1991) 137-139.
13. N.J. Higham, Perturbation theory and backward error for AX - XB = C, BIT 33 (1993) 124-136.
14. N.J. Higham, FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation, ACM Trans. Math. Software 14 (1988) 381-396.
15. B. Kågström and L. Westin, Generalized Schur methods with condition estimators for solving the generalized Sylvester equation, IEEE Trans. Automat. Control 34 (1989) 745-751.
16. B. Kagström and P. Poromaa, LAPACK-style algorithms and software for solving the generalized Sylvester equation and estimating the separation between regular matrix pairs, ACM Trans. Math. Software 22 (1996) 78-103.
17. P. Lancaster and M. Tismenetsky, The Theory of Matrices (Academic Press, Orlando, 2nd ed., 1985).
18. T = -C, SIAM J. Appl. Math. 18 (1970) 704-714.
19. Working Group on Software (WGS), Implementation and documentation standards, WGS-Report 90-1, Eindhoven/Oxford (1990).