Is nonnormality a serious computational difficulty in practice?

摘要

The departure from normality of a matrix plays an essential role in numerical matrix computations since it rules the spectral instability. But this first consequence of high nonnormality was for long considered by practitioners as a mathematical oddity, since such matrices were not often encountered in practice. It appears now that more and more matrices, which have a possibly unbounded departure from normality, emerge in the mdoeling of physical problems at the edge of instability. They challenge many robust numerical codes because of a second and recently exposed consequence of nonnormality: the possible deterioration of the backward stability for algorithms (Chaitin-Chatelin and Fraysse (1996)).