Existence criteria for partial matrix factorizations in iterative methods

Conditions which prevent a factorization iterative method from failing, or factorizability conditions, are investigated for a class of algorithms called here the Oliphant–Buleev (or O.B.) methods; in particular, criteria are obtained for generalized forms of the Stone and Buleev factorization methods. Extensions of these results to block factorization schemes are developed while convergence properties are obtained for symmetric point O.B. algorithms.Copyright © 1976 Society for Industrial and Applied Mathematics.