- If you had a system with 10000 variables, would you think to use a direct method or an iterative method?
- Name three iterative methods
- Which is for illustration and which would you actually use?
- Write down the formulas for the three iterative methods discussed in terms of components $x_i$, $a_{i,j}$, $b_i$
- How are iterative methods understood in terms of $x_i^{k+1} = x_i^k+\Delta x_i$?
- How is this modified for the SOR method?
- What do we call the parameter used to control strength or magnitude of the effect in SOR?
- What convergence criteria is used? (There is more than one right answer, but what is a good one?)
- Write a Python code to solve an iterative system using one of the three methods.
- A convergence analsysis was presented that made use of an eigenvector expansion. How does that simplify the analysis in terms of the behavior of the error?