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On the sensitivity of the solution of the generalized Lyapunov equation
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Some results on the sensitivity of the solution of thegeneralized Lyapunov equationAn-1X + An-2XA* + ㆍㆍㆍ + X(A*)n-1 = B,are shown follow easily from well-known theorems in functional analysis.
Abstract
Some results on the sensitivity of the solution of thegeneralized Lyapunov equationAn-1X + An-2XA* + ㆍㆍㆍ + X(A*)n-1 = B,are shown follow easily from well-known theorems in functional analysis.
참고문헌 (7)
- T. Ando, "Majorization, Doubly stochastic matrices and comparison of eigenval- ues", Linear Algebra Appl, 118, pp.163~248 (1989)
- R. Bhatia, "A note on the Lyapunov equation", Linear Algebra Appl, 259, pp.71~76 (1997)
- R. Bhatia, "The operator equation Σni=0 An-iXBi = Y", Expo. Math, 27(3), pp.251~255 (2009)
- G. Hewer, "The sensitivity of the stable Lyapunov equation", SIAM J. Control Optim, 26, pp.321~344 (1988)
- M. Reed, "Methods of Morder Mathematical Physics II" (1975), Academic
- W. Rudin, "Functional Analysis" (1973), McGraw-Hill
- B. Rosso, "A note on unitary operator in C*-algebras", Duke Math. J, 33, pp.413~416 (1966)
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