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The Algebraic Theory of Matrix Polynomials
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 matrixExpand
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Algorithms for solvents of matrix polynomials
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 certainExpand
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A Brief Survey of Convergence Results for Quasi-Newton Methods
This paper highlights the important theoretical developments in the study of quasi-Newton or update methods and suggests avenues for future research. Expand
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On Newton-like methods
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'SExpand
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On the Matrix Polynomial, Lambda-Matrix and Block Eigenvalue Problems
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. TheExpand
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A Stationary Newton Method for Nonlinear Functional Equations
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 convergenceExpand
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A Brief Introduction to Quasi-Newton Methods
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