Original scientific paper

The perturbation bound for the solution of the Lyapunov equation

Ninoslav Truhar

Abstract

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 = mΣk=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.

Keywords

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

Hrčak ID:

12607

URI

https://hrcak.srce.hr/12607

Publication date:

31.5.2007.

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