A LINPACK-style condition estimator for the equation AX-XB^{T} = C
Ralph E. Byers · IEEE Transactions on Automatic Control · 1984
Estimation of the condition number ofAX- XB^{T} = Crequires an approximation of the smallest l2singular value of the linear transformationX \rightarrow AX - XB^{T}. The approximation is obtained from a step of inverse iteration applied to a heuristically chosen starting matrix. In the style of LINPACK, the cost of the estimator is kept down by using the same matrix factorizatlons to make the estimate as are used to solveAX - XB^{T} = C. Computational experiments verify its reliability.