Residual bounds of approximate solutions of the algebraic Riccati equation

Numerische Mathematik

Volumn 76, Issue 2, 1997, Pages 249-263

  Sun, Ji Guang ^a  

^a UMEÅ UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031508420     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050262     Document Type: Article

References (18)

1. Byers, R. (1985): Numerical condition of the algebraic Riccati equation. In: B. N. Datta (ed.) Linear Algebra and Its Role in System Theory 47, pp. 35-49, Providence, RI: AMS Contemporary Mathematics Series
2. Byers, R., Nash, S. (1987): On the singular "vectors" of the Lyapunov operator. SIAM J. Alg. Disc. Meth. 8, 59-66
3. Chen, C.-H. (1988): Perturbation analysis for solutions of algebraic Riccati equations. J. Comput. Math. 6, 336-347
4. Ghavimi, A.R., Laub, A.J.: Backward error, sensitivity, and refinement of computed solutions of algebraic Riccati equations, to appear in Numerical Linear Algebra with Applications.
5. Higham, N.J. (1993): Perturbation theory and backward error for AX-XB = C. BIT 33, 124-136
6. Kenney, C., Hewer, G. (1990): The sensitivity of the algebraic and differential Riccati equations. SIAM J. Control. Optim. 28, 50-69
7. Kenney, C., Laub A.J., Wette, M. (1990): Error bounds for Newton refinement of solutions to algebraic Riccati equations. Math. Contr. Signals Syst. 3, 211-224
8. Lancaster, P., Tismenetski, M. (1985): The Theory of Matrices. Academic Press, New York
9. Laub, A.J. (1979): A Schur method for solving algebraic Riccati equations. IEEE Trans. Aut. Control, AC-24, 913-921
10. Paige, C.C., Van Loan, C. (1981): A Schur decomposition for Hamiltonian matrices. Linear Algebra Appl. 41, 11-32
11. Rigal, J.L., Gaches J. (1967): On the computability of a given solution with the data of a linear system. J. Assoc. Comput. Mach. 14, 90-101
12. Stewart, G. W. (1973): Error and perturbation bounds for subspaces associated with certain eigenvalue problems. SIAM Rev. 15, 727-764
13. Stewart, G.W., Sun, J.-G. (1990): Matrix Perturbation Theory, Academic Press, New York
14. Sun, J.-G. (1993): Backward perturbation analysis of certain characteristic suhspaces. Numer. Math. 65, 357-382
15. Van Dooren P. (1981): A generalized eigenvalue approach for solving Riccati equations. SIAM J. Sci. Stat. Comput. 2, 121-135
16. Van Loan, C. (1985): How near is a stable matrix to an unstable matrix? Contemporary Mathematics 47, 465-478
17. Xu, H.-G., Lu, L.-Z. (1995): Properties of a quadratic matrix equation and the solution of the continuous-time algebraic Riccati equation. Linear Algebra Appl. 222, 127-145
18. Xu, S.-F.: Sensitivity analysis of the algebraic Riccati equations, to appear in Numer. Math.