Retracing the residual curve of a Lyapunov equation solver

Abstract

This is an accepted version of a paper published in BIT Numerical Mathematics. This paper has been peer-reviewed but does not include the final publisher proof-corrections or journal pagination.Citation for the published paper: Kjelgaard Mikkelsen, C. Retracing the residual curve of a Lyapunov equation solver Carl Christian Kjelgaard MikkelsenReceived: date / Accepted: date Abstract Let A ∈ R n×n and let B ∈ R n×p and consider the Lyapunov matrix equation AX + XA T + BB T = 0. If A + A T < 0, then the extended Krylov subspace method (EKSM) can be used to compute a sequence of low rank approximations of X. In this paper we show how to construct a symmetric negative definite matrix A and a column vector B, for which the EKSM generates a predetermined residual curve.