An iterative method to solve the algebraic eigenvalue problem (Q1381398)

An eigenvalue algorithm based on perturbation expansions is derived. It partitions the matrix into the sum of a diagonal and a perturbation part. An estimate of a diagonalization of the perturbation is computed and applied. Under favorable circumstances, the matrix after transformation has a more dominant diagonal part. Asymptotically it behaves like a Jacobi algorithm, but conditions for convergence are not derived. Numerical experiments on Hilbert matrices with enlarged diagonal elements are reported.