engleski

The perturbation bound for the solution of the Lyapunov equation

We present the first order error bound for the Lyapunov equation AX +XA* = − GG*, where A is perturbed to A+δ A. We use the structure of the solution of the Lyapunov equation X = \sum_{;k=1};^m W_k W_k^{;*}; , where W_k 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 {;p_1, ... , p_m}; = 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.

Lyapunov equation; perturbation theory; perturbation bound; low rank Cholesky factor ADI method

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