# Iterative Methods for Solving $$A\mathbf{x} = b$$

Module with 2 tutorials, with exercises and a Java applet, for iterative solution methods

Identifier:
http://faculty.pepperdine.edu/dstrong/Java/IterativeMethods/
Rating:
Creator(s):
David M. Strong
Cataloger:
David Strong
Publisher:
Pepperdine University
Rights:
David M. Strong
Format Other:
Java may need to be enabled in the Java Console

## Comments

### well-written introduction to numerical solution of systems

This module contains a well-written introduction to numerical solution of systems of linear equations and a Java applet. The text has a two-part tutorial on the Jacobi and Gauss-Seidel methods, convergence analysis, and the SOR method. Homework exercises are included. The applet allows the user to input the 2x2 coefficient matrix A and constant vector b in R^2 for the system Ax=b, to make an initial guess at the solution, and to input which of the three methods the user wishes to use. The applet then computes a single iteration of the selected methods and allows the user to continue iteration by iteration. A graph displays the sequence of approximate solutions as points in R^2 along with the exact solution to the system.

### a rare find

An applet for iterative solution methods (Jacobi, Gauss-Seidel, and SOR) is a rare find. The graphics can help one learn about the geometric features of these methods. It is unfortunate that the applet is limited to $$2\times2$$ systems. A version for higher systems (without the graphics) would be a nice addition.