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Browsing by Author "Dennis, John E., Jr."
Now showing items 117 of 17

Algorithms for Nonlinear Problems Which Use DiscreteApproximations to Derivatives
Dennis, John E., Jr. (Cornell University, 197105)The most desirable algorithms for nonlinear programming problems call for obtaining the gradient of the objective and the Jacobian of the constraint function. The analytic form is often impossible and almost always impractical ... 
A Brief Introduction to QuasiNewton Methods
Dennis, John E., Jr. (Cornell University, 197711)NO ABSTRACT SUPPLIED 
A Brief Survey of Convergence Results for QuasiNewton Methods
Dennis, John E., Jr. (Cornell University, 197505)This paper highlights the important theoretical developments in the study of quasiNewton or update methods and suggests avenues for future research. An attempt is made to present this material in a way reasonably ... 
A Characterization of Superlinear Convergence and its Application to QuasiNewton Methods
Dennis, John E., Jr.; More, Jorge J. (Cornell University, 197301)Let F be a mapping from real ndimensional Euclidean space into itself. Most practical algorithms for finding a zero of F are of the form $x_{k+1} = x_{k}  B_{k}^{1_{Fx_{k}}}$ where $\{B_{k}\}$ is a sequence of nonsingular ... 
A Characterization of Superlinear Convergence and its Application to QuasiNewton Methods
Dennis, John E., Jr.; More, Jorge J. (Cornell University, 197301)Let F be a mapping from real ndimensional Euclidean space into itself. Most practical algorithms for finding a zero of F are of the form $x_{k+1} = x_{k}  B_{k}^{1_{Fx_{k}}}$ where $\{B_{k}\}$ is a sequence of nonsingular ... 
A Continuous Analogue Analysis of Nonlinear Iterative Methods
Boggs, Paul T.; Dennis, John E., Jr. (Cornell University, 197403)This paper applies the asymptotic stability theory for ordinary differential equations to Gavurin's continuous analogue of several wellknown nonlinear iterative methods. In particular, a general theory is developed which ... 
Least Change Secant Updates for QuasiNewton Methods
Dennis, John E., Jr.; Schnabel, Robert B. (Cornell University, 197806)In many problems involving the solution of a system of nonlinear equations, it is necessary to keep an approximation to the Jacobian matrix which is updated at each iteration. Computational experience indicates that the ... 
A New Algorithm for Nonlinear Least Squares Curve Fitting
Brown, Kenneth M.; Dennis, John E., Jr. (Cornell University, 197003)NO ABSTRACT SUPPLIED 
On NewtonLike Iteration Functions: General Convergence Theorems and a Specific Algorithm
Brown, Kenneth M.; Dennis, John E., Jr. (Cornell University, 196806)On NewtonLike Iteration Functions: General Convergence Theorems and a Specific Algorithm 
On Some Methods Based on Broyden's Secant Approximation to the Hessian
Dennis, John E., Jr. (Cornell University, 197107)NO ABSTRACT SUPPLIED 
On the Convergence of Broyden's Method for Nonlinear Systems of Equations
Dennis, John E., Jr. (Cornell University, 196910)On the Convergence of Broyden's Method for Nonlinear Systems of Equations 
On the Local Convergence of Broyden's Method for NonlinearSystems of Equations
Dennis, John E., Jr. (Cornell University, 196910)The purpose of this paper is to present an alternate to the proof given in [3] of the local convergence of Broyden's method. The result was stated there as a simple corollary of a Kantorovichtype theorem for the method. ... 
On the Local Convergence of Nonlinear Successive Overrelaxation and Related Methods
Brown, Kenneth M.; Dennis, John E., Jr. (Cornell University, 196910)On the Local Convergence of Nonlinear Successive Overrelaxation and Related Methods 
On the Matrix Polynomial, LamdaMatrix and Block Eigenvalue Problems
Dennis, John E., Jr.; Traub, J.F.; Weber, R.P. (Cornell University, 197109)A matrix $S$ is a solvent of the matrix polynomial $M(X) \equiv X^{m} + A_{1}X^{m1} + \cdots + A_{m}$, if $M(S) = \stackrel{0}{=}$, where $A_{1}, X$ and $S$ are square matrices. We present some new mathematical results ... 
QuasiNewton Methods, Motivation and Theory
Dennis, John E., Jr.; More, Jorge J. (Cornell University, 197411)This paper is an attempt to motivate and justify quasiNewton methods as useful modifications of Newton's method for general and gradient nonlinear systems of equations. References are given to ample numerical justification; ... 
Some Minimal Properties of the Trapezoidal Rule
Dennis, John E., Jr.; Sweet, Roland A. (Cornell University, 197006)NO ABSTRACT SUPPLIED 
An Unconstrained Optimization Algorithm Which Uses Function and Gradient Values
Dennis, John E., Jr.; Mei, Howell HungWei (Cornell University, 197506)A new method for unconstrained optimization is presented. It consists of a modification of Powell's 1970 dogleg strategy with the approximate Hessian given by Davidson's 1975 updating scheme which uses the projections ...