Componentwise perturbation analysis for the generalized Schur decomposition

By defining two important terms called basic perturbation vectors and obtaining their linear bounds, we obtain the componentwise bounds for unitary factors upper triangular of generalized Schur decomposition. The diagonal elements invariant subspace are also derived. From former, present an bound a condition number eigenvalue. Furthermore, with numerical iterative method, nonlinear decomposition provided. Numerical examples given to test obtained bounds. Among them, compare our eigenvalue counterparts in literature. results show that they very close each other but don’t contain information on left right eigenvectors.