Computing Derivatives of Eigenvalues and Eigenvectors by Simultaneous Iteration

A simultaneous iteration scheme of Andrew is analysed and extended, and developed into an effective algorithm for numerical computation of partial derivatives of several eigenvalues and eigenvectors of a matrix which depends on a number of parameters. It is shown that, with exact computation, application of either the vector e-algorithm or the topological e-algorithm to this method produces the exact solution in a small number of steps. Numerical tests confirm the viability of the method. 1