Retracing the residual curve of a Lyapunov equation solver

Abstract

Let A∈ℝn×n and let B∈ℝn×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.