Resolvent estimates and eigenvalue decay of solutions to Lyapunov operator equations (CROSBI ID 616915)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
Podaci o odgovornosti
Grubišić, Luka ; Kressner, Daniel
engleski
Resolvent estimates and eigenvalue decay of solutions to Lyapunov operator equations
We analyze the eigenvalue decay of the solution to operator Lyapunov equations with right-hand sides of finite rank. We show that the k-th eigenvalue decays exponentially in sqrt(k), provided that the involved operator A generates an exponentially stable continuous semigroup, and A is either self-adjoint or a scalar type operator. We present an analysis in a scale of Hilbert spaces and allow for right hand sides which are themselves unbounded but are of finite rank in a relative sense. We present numerical experiments to assess the sharpness of the estimates on the rate of the eigenvalue decay.
Balanced truncation ; Exponential decay ; Lyapunov equation
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Podaci o prilogu
1-1.
2014.
objavljeno
Podaci o matičnoj publikaciji
Podaci o skupu
Pseudospectra of operators: spectral singularities, semiclassics, pencils and random matrices
pozvano predavanje
15.09.2014-20.09.2014
Edinburgh, Ujedinjeno Kraljevstvo