The perturbation bound for the solution of the Lyapunov equation ∗
نویسنده
چکیده
We present the first order error bound for the Lyapunov equation AX +XA∗ = −GG∗, where A is perturbed to A+ δA. We use the structure of the solution of the Lyapunov equation X = m ∑ k=1 WkW ∗ k , where Wk is the k-th matrix obtained by the Low Rank Cholesky Factor ADI (LRCF-ADI) algorithm using the set of ADI parameters equal to exact eigenvalues of A, that is with ADI parameters {p1, . . . , pm} = σ(A). Our bound depends on the structure of the right-hand side G of the Lyapunov equation, and sometimes it can be sharper than the classical error bounds.
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