An extrapolation method for computing derivatives of eigensystems

An explicit annihilation procedure, based on an iterative scheme of Rudisill and Chu, is proposed for computing derivatives of eigenvalues and eigenvectors of parameter-dependent matrices. It is shown that, with exact arithmetic, the method produces the exact solution. Numerical results establish the viability of the method in the presence of roundoff, even for subdominant eigenvalues. The method is compared with some alternative methods.