NON-LINEAR BOUNDS FOR THE GENERALIZEDEIGENSYSTEM OF A MATRIX PENCIL WITH DISTINCTEIGENVALUES

摘要

In this paper a non-local sensitivity analysis of the generalized eigensystem (eigenvectors andeigenvalues) of an n ? n matrix pencil A - λB with pairwise distinct eigenvalues is made. By rewritingthe perturbed problem as an operator equation and using the technique of Lyapunov majorantsnon-local non-linear bounds are established. An example demonstrates the effectiveness of theestimates proposed.