Small-sample statistical condition estimation of large-scale generalized eigenvalue problems

We consider the evaluation of the sensitivity or condition number of (generalized) eigenvalue problems for a large and sparse real matrix (or matrix pair) in Rn×nRn×n, through some (coupled) Sylvester equation using Newton’s method. The technique of the statistical condition estimation has been adapted to the sensitivity of symmetric matrices as well as general matrices with special structures under some assumptions on various types of perturbations.