A continuous approximation to the generalized Schur decomposition

AbstractWe consider the problem of approximating the generalized Schur decomposition of a matrix pencil A − λB by a family of differentiable orthogonal transformations. It is shown that when B is nonsingular this approach is feasible and can be fully expressed as an autonomous differential system. When B is singular, we show that the location of zero diagonal entries of B affects the feasibility of such an approach, and hence we conclude that at least the QZ algorithm cannot be extended continuously