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Iterative Methods for Solving Ax = b - Information on the Java Applet

Author(s): 
David M. Strong
How to access and run the applet:
  • You can access the applet here . There are also links to it in the problems for which it is used.

  • The Java Plug-in (version 1.4 or higher) is required to use the applet. If you don’t have this plug-in, visit Sun Microsystems' Java Download page, and you should get it automatically -- just follow the prompts and steps.

The applet is designed for solving a 2 x 2 system of equations using the Jacobi, Gauss-Seidel and/or SOR Methods.

How to use the applet:

  • Enter the values for the matrix A, the vector b, and the initial guess x(0).

  • Under Methods to use, click the Jacobi, Gauss-Seidel, and/or SOR boxes to use the desired iterative method(s). If you select the SOR Method, you should also select a value for ω.

  • To iterate the selected method(s), under Do iteration using, click the Initial guess button to do the first iteration using x(0), and then click the Current approximation button to do subsequent iterations using the most recent approximation from each selected method. You can select or unselect any method at any time. The applet stores the results of the iterations for each method even if they are not currently being displayed.

  • The applet’s table of data will give you
    • the current approximation x(k) = (x1(k), x2(k)),
    • the current error error(k) = (x1truex1(k), x2truex2(k)), and
    • the norm of the current error ||error(k)||.
  • Notice the color coordination of the applet. For example, everything related to the True solution is in green, everything related to the Gauss-Seidel Method is in purple, and so on.

  • When changing the minimum and maximum x1 and x2 values (in the bottom left part of the applet) for the graphing window, you must press Enter to make those changes take effect. You can also use the zoom buttons or set your own viewing window by pressing and dragging the left mouse button on the graph (experiment to see this feature).

  • The applet is designed to be very robust, including checking for bad input. However, like any software or other technology, it is not completely fail-proof. For example, working with extremely small or large numbers could result in inaccurate results.

David M. Strong, "Iterative Methods for Solving [i]Ax[/i] = [i]b[/i] - Information on the Java Applet," Loci (July 2005)

JOMA

Journal of Online Mathematics and its Applications

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