SMALL-SAMPLE STATISTICAL ESTIMATES FOR THE SENSITIVITY OF EIGENVALUE PROBLEMS

In this paper a new approach to the evaluation of sensitivity or condi tion of eigenvalue problems is proposed. This approach is applicable t o general nonsymmetric matrices as well as to matrices with special st ructure and is suitable for various types of perturbations. In particu lar, the important class of componentwise relative perturbations can e asily be handled for a general matrix. This cannot be done satisfactor ily with other currently available methods. The sensitivity evaluation is based on the recently introduced technique of small-sample statist ical estimation for the local sensitivity of a large variety of functi ons.