Computation of mixed partial derivatives of eigenvalues and eigenvectors by simultaneous iteration

Abstract

A new simultaneous iteration method is presented for computing mixed second-order partial derivatives of several eigenvalues and the corresponding eigenvectors of a matrix which depends smoothly on some real-valued design parameters. Numerical results illustrate the viability of the method, and show it to be more stable than a previously published iterative method for derivatives of eigenvectors corresponding to subdominant eigenvalues. Copyright © 1999 John Wiley & Sons, Ltd.