Relaxation methods for an eigenproblem
W. Kahan · 1966
A theory is developed to account for the convergence properties of certain relaxation iterations which have been widely used to solve the eigenproblem $(A - \lambda B) \underline{x} = 0, \underline{x} eq 0, with large symmetric matrices A and B and positive definite B. These iterations always converge, and almost always converge to the right answer. Asymptotically, the theory is essentially that of the relaxation iteration applied to a semi-definite linear system discussed in the author''s previous report [Stanford University Computer Science Department report CS45, 1966].