Project 20 looks again at the problem of solving huge linear system, which often arise as part of the solution of a discretized system of partial differential equations. In project 15, we examined direct methods for solving such systems. In this project, we turn to another family of techniques known as iterative methods. The characteristic of iterative methods for solving A*x=b is that an initial guess for x is supplied, and then the method is repeatedly applied to the current guess to derive what should be an improved estimate.
The case study involves discretized versions of the heat equation for a square plate, and for a square plate with a hole in it. The iterative techniques considered include stationary methods such as the Gauss-Seidel iteration, and the preconditioned conjugate gradient method. The effect of the preconditioner is also examined.
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