Math and lab clarification.

[mrshannon]

I have done the setup and am at the Jacobi part, which is taught in graduate numerical methods (which is a significant math class, which is not a prerequisite for this course). The math required for this homework was not covered in the lectures in enough detail for someone who has not had that level of math.

The homework says to use Jacobi and Gauss-Seidel not norms and point-wise updates using neighbors.

If it was covered in the labs which distance students do not have access to then it should not be part of the homework.

[jedbrown]

The Jacobi method was described in lecture as u_{k+1} = u_k + omega * D^{-1} R(u_k) where D is the matrix diagonal and R(u_k) is the residual function you have been given in the homework. We drew pictures of this during the lab that introduced the homework, and discussed a number of questions. If you don't attend lab (distance section or otherwise), I would expect that you work through it on your own and ask questions, either in this forum or by directly discussing with other students. Respectfully, the best time to ask questions about how to start is in the first few days so that I can incorporate visual discussion into lecture. I realize I may not have communicated this clearly and will do my best to answer questions in this forum.

As for prerequisites, this class is about scientific computing, each aspect of which uses math (often different flavors of math). There will be concepts you haven't seen; I'll provide introductions and pointers to further references. You won't need to dive in deep with the math (I don't ask you to derive equations, prove theorems, etc.), but you will need to have an open mind, be willing to read supplementary resources, and strive to ask questions.

As for this particular homework, you've been given a function Residual that evaluates b - A u where A is the matrix representation of the stencil operation

[0  -1   0;
-1   4  -1;
 0  -1   0]

It shows the relation between stencils and matrices; Jacobi is a small modification to the above, and Gauss-Seidel can be thought of as a triangular solve or as sweeping through the grid like in Residual, but where the updates are in-place (so that subsequent points use the "new" values of u).

[mrshannon]

Please show where in the course description it says that distance students would be disadvantaged.

[jedbrown]

That is not the intent, but you absolutely need to take the initiative to read and ask questions because you aren't in the room talking with classmates during the lab. Suggestions to improve format for distance section labs would be greatly appreciated.