Retracing the residual curve of a Lyapunov equation solver (Q657886)

Let \(A\in \mathbb R^{n\times n }\) and let \(B\in \mathbb R^{n\times p }\) 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 the construction of a symmetric negative definite matrix \(A\) and a column vector \(B\), for which the EKSM generates a predetermined residual curve is illustrated.