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The Algebraic Theory of Matrix Polynomials
• Mathematics
• 1 December 1976
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
• Mathematics
• 1 June 1978
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
• Mathematics
• 17 December 1971
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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