cswiercz
commented
8 years ago Good question. Looking at the homework assignment I see that I hadn't requested that the jacobi_iteration or gauss_seidel_iteration functions check if the input matrix is SDD or DD. Therefore, your implementations of these functions need not perform the check before iteration to a solution, x.
That being said, the tests we perform will be using matrices that satisfy the necessary conditions for convergence.
From a practical standpoint, it might be preferred in this case for the "user" to ensure that the input matrix satisfies the required conditions before calling jacobi_iteration, etc. (Imagine you're writing a linear algebra library for other people to use.) If A is huge it takes a good O(n^2) work just to verify SDD/DD. However, depending on the problem such a check might be mission critical.
In this homework assignment, this check is not mission critical.
For the Jacobi method to converge, we must guarantee strict diagonal dominance of the input matrix. As mentioned in the problem statement, Gauss-Seidel only requires diagonal dominance. Should we reject input matrices with only dominant -- but not strictly dominant -- diagonals in Gauss-Seidel?