On the eigenvalue decay of solutions to operator Lyapunov equations (CROSBI ID 209600)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Grubišić, Luka ; Kressner, Daniel
engleski
On the eigenvalue decay of solutions to operator Lyapunov equations
This paper is concerned with the eigenvalue decay of the solution to operator Lyapunov equations with right-hand sides of finite rank. We show that the k-th (generalized) eigenvalue decays exponentially in -sqrt(k), provided that the involved operator A generates an exponentially stable analytic semigroup, and A is either self-adjoint or diagonalizable with its eigenvalues contained in a strip around the real axis. Numerical experiments with discretizations of 1D and 2D PDE control problems confirm this decay.
Balanced truncation ; Exponential decay ; Lyapunov equation
Rad je sufinanciran i po Sveučilištu u Zagrebu, projekti br. 4.1.2.3. i K2.101.
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Podaci o izdanju
73
2014.
42-47
objavljeno
0167-6911
1872-7956
10.1016/j.sysconle.2014.09.006