Upper eigenvalue bounds for pencils of matrices

Eigenvalue bounds are obtained for pencils of matrices A - vB where A is a Stieltjes matrix and B is positive definite, under assumptions suitable for the estimation of asymptotic convergence rates of factorization iterative methods, where B represents the approximate factorization of A. The upper bounds obtained depend on the "connectivity" structure of the matrices involved, which enters through matrix graph considerations; in addition, a more classical argument is used to obtain a lower bound. Potential applications of these results include a partial confirmation of Gustafsson's conjecture concerning the nonnecessity of Axelsson's perturbations. © 1984.SCOPUS: ar.j