Now showing items 1-10 of 10

• #### The Application of Variational Inequalities to Complementarity Problems and Existence Theorems ﻿

(Cornell University, 1971-10)
• #### Estimation of Sparse Hessian Matrices and Graph Coloring Problems ﻿

(Cornell University, 1982-12)
Large scale optimization problems often require an approximation to the Hessian matrix. If the Hessian matrix is sparse then estimation by differences of gradients is attractive because the number of required differences ...
• #### Nonlinear Generalizations of Matrix Diagonal Dominance with Application to Gauss-Seidel Iterations ﻿

(Cornell University, 1971-01)
A new class of nonlinear mappings is introduced which contains, in the linear case, the strictly and irreducibly diagonally dominant matrices as well as other classes of matrices introduced by Duffin and Walter. We then ...
• #### On the Global Convergence of Broyden's Method ﻿

(Cornell University, 1974-10)
We consider Broyden's 1965 method for solving nonlinear equations. If the mapping is linear, then a simple modification of this method guarantees global and Q-superlinear convergence. For nonlinear mappings it is shown ...
• #### Quasi-Newton Methods, Motivation and Theory ﻿

(Cornell University, 1974-11)
This paper is an attempt to motivate and justify quasi-Newton methods as useful modifications of Newton's method for general and gradient nonlinear systems of equations. References are given to ample numerical justification; ...
• #### Software For Estimating Sparse Hessian Matrices ﻿

(Cornell University, 1985-01)
The solution of a nonlinear optimization problem often requires an estimate of the Hessian matrix for a function $f$. In large scale problems the Hessian matrix is usually sparse, and then estimation by differences of ...
• #### Software for Estimating Sparse Jacobian Matrices ﻿

(Cornell University, 1982-06)
In many nonlinear problems it is necessary to estimate the Jacobian matrix of a nonlinear mapping $F$. In large scale problems the Jacobian of $F$ is usually sparse, and then estimation by differences is attractive because ...