Error Bound for Computed Eigenvectors.

LAPACK [12] presents a few error bounds for computed eigenvectors of the (small) dense GNHEP of a regular matrix pair $\{A,B\}$, assuming the availability of the generalized Schur decomposition of the pair. Interested readers are referred to [425,431]. It is generally not possible to assess the accuracy of computed eigenvectors of the large sparse problems with only partial information of a few eigenvalues and eigenvectors.