Project 16 looks at a huge linear system A*x=b. The size of the system means we need to come up with ways of reducing the storage space and the time requirements, which would not be an issue for smaller matrices.
In this case, the matrix comes from the discretized Poisson equation, which was previously studied in Peoject 15. The structure results in a matrix that is block tridiagonal, with constant blocks.
Project 15 took advantage of the fact that most of this matrix was zero. Now, we are going to look more closely at the specific structure of the nonzero elements; since they have a pattern, we can obviously save even more storage space. But even better, we may be able to figure out a faster method of solving the linear system.
The quest for a faster solution method starts by writing the linear system in terms of the nonzero blocks, and then rearranging these so that we can see that we have what is called a Sylvester equation.
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