# Nonlinear Difference Equations and Gauss-Seidel Type Iterative Methods

@article{Ortega1966NonlinearDE, title={Nonlinear Difference Equations and Gauss-Seidel Type Iterative Methods}, author={James M. Ortega and Maxine L. Rockoff}, journal={SIAM Journal on Numerical Analysis}, year={1966}, volume={3}, pages={497-513} }

Asymptotic rate of convergence of Gauss-Seidel type iterative processes for nonlinear difference equations

## 73 Citations

### Monotone Iterations for Nonlinear Equations with Application to Gauss-Seidel Methods

- Mathematics
- 1967

Monotone iterations for nonlinear elliptic differential equations in boundary-value problems applied to Gauss-Seidel methods

### On nonlinear SOR-like methods, II — Convergence of the SOR-Newton method for mildly nonlinear equations

- Mathematics
- 1997

This is a continuation of a previour paper [22]. Local and global convergence theorems are established for the SOR-Newton method applied to a system of mildly nonlinear equations which arises from…

### Use of fast direct methods for mildly nonlinear elliptic difference equations

- Mathematics
- 1982

We consider in a rectangle the dirichelet mildly nonlinear elliptic boundary value problem.The numerical solution by finite-difference equations leads to the problem of solving special nonlinear…

### Accelerating the Convergence of Discretization Algorithms

- Computer Science, Mathematics
- 1967

Acceleration techniques for discretization algorithms used in the approximate solution of nonlinear operator equations are considered and applied to the approximation solution of mildly nonlinear elliptic equations by finite differences.

### Perturbed iterative solution of nonlinear equations with applications to fluid dynamics

- Mathematics
- 1977

### Numerical solution of the minimal surface equation

- Mathematics
- 1967

The minimal surface equation is solved numerically by use of the method studied previously by the author for solving the two -dim en-sirinal nonlinear magnetostatic-field equation. The method…

### Fast local convergence with single and multistep methods for nonlinear equations

- MathematicsThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- 1975

Abstract Methods which make use of the differential equation ẋ(t) = −J(x)−1f(x), where J(x) is the Jacobian of f(x), have recently been proposed for solving the system of nonlinear equations f(x) =…

### Convergence and Stability of Line Search Methods for Unconstrained Optimization

- Mathematics
- 2013

This paper explores the stability of general line search methods in the sense of Lyapunov, for minimizing a smooth nonlinear function. In particular we give sufficient conditions for a line search…

### Convergence and Stability of Line Search Methods for Unconstrained Optimization

- MathematicsActa Applicandae Mathematicae
- 2013

This paper explores the stability of general line search methods in the sense of Lyapunov, for minimizing a smooth nonlinear function. In particular we give sufficient conditions for a line search…

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- Mathematics
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Matrix Properties and Concepts.- Nonnegative Matrices.- Basic Iterative Methods and Comparison Theorems.- Successive Overrelaxation Iterative Methods.- Semi-Iterative Methods.- Derivation and…