Institution: Stanford University, Department of Computer Science

Title: Relaxation methods for an eigenproblem

Author: Kahan, William

Date: August 1966

Abstract: 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} \neq 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].

http://i.stanford.edu/pub/cstr/reports/cs/tr/66/44/CS-TR-66-44.pdf