Solving the inverse eigenvalue problem via the eigenvector matrix (Q803722)

A numerical algorithm for the inverse eigenvalue problem for symmetric matrices is proposed, based on continually updating the eigenvector matrix using plane rotations. The idea behind this algorithm is to utilize the matrix formed from the Rayleigh quotients of the eigenvectors with respect to each of the basis matrices involved. The computational questions involved in this approach are examined in detail. Numerical examples are given which demonstrate that the new algorithm is much more robust than the Newton's method.