A matrix S is a solvent of the matrix polynomial $M(X) = A_0 X^m + \cdots + A_m $ if $M(S) = 0$ where $A_i ,X,S$ are square matrices. In this paper we develop the algebraic theory of matrix… Expand

In an earlier paper we developed the algebraic theory of matrix polynomials. Here we introduce two algorithms for computing “dominant” solvents. Global convergence of the algorithms under certain… Expand

This paper highlights the important theoretical developments in the study of quasi-Newton or update methods and suggests avenues for future research.Expand

where x 0 is prechosen and M is some, not necessarily continuous, correspondence between /2 o and L(Y, X). For a practical problem, such as the simultaneous solution of nonlinear equations, NEWTON'S… Expand

Abstract : A matrix S is a solvent of the matrix polynomial M(X) identically equal to X sup m + A(sub 1) X sup(M - 1) + ... + A sub m, if M(S) = 0, where A sub i, X and S are square matrices. The… Expand

where M E [Y X], the Banach space of bounded linear operators from Y into X. In the special case X = R = Y, [Y -> X] = R and so (2) reduces to (1). M. Ghinea [5, Theorem 1, p. 10] has a convergence… Expand