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The Algebraic Theory of Matrix Polynomials
- J. E. Dennis, J. Traub, R. Weber
- 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 matrix… Expand
Algorithms for solvents of matrix polynomials
- J. E. Dennis, J. Traub, R. Weber
- 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 certain… Expand
A Brief Survey of Convergence Results for Quasi-Newton Methods
- J. E. Dennis
- Computer Science
- 1 May 1975
TLDR
- 22
- 3
On Newton-like methods
- J. E. Dennis
- Mathematics
- 1 May 1968
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
On the Matrix Polynomial, Lambda-Matrix and Block Eigenvalue Problems
- J. E. Dennis, J. Traub, R. Weber
- 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. The… Expand
- 19
- 1
Practical Methods of Optimization, Vol. 1: Unconstrained Optimization (R. Fletcher)
- J. E. Dennis
- Mathematics
- 1982
A Stationary Newton Method for Nonlinear Functional Equations
- J. E. Dennis
- Mathematics
- 1 June 1967
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