Small-Sample Statistical Estimates for the Sensitivity of Eigenvalue Problems
Thorkell Gudmundsson · SIAM Journal on Matrix Analysis and Applications · 1997
In this paper a new approach to the evaluation of sensitivity or condition of eigenvalue problems is proposed. This approach is applicable to general nonsymmetric matrices as well as to matrices with special structure and is suitable for various types of perturbations. In particular, the important class of componentwise relative perturbations can easily be handled for a general matrix. This cannot be done satisfactorily with other currently available methods. The sensitivity evaluation is based on the recently introduced technique of small-sample statistical estimation for the local sensitivity of a large variety of functions.