Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 67 / 5 / a / Solution

Assume $n\ge 3$ and use periodic indices for the Jacobi method. At iteration $r$, it isAll values on its right side belong to the old iterate. For lexicographic Gauss-Seidel iteration, compute in the order $1,\dots ,n$ and use a newly available coordinate immediately:The wrap-around term in the last row uses the new $x_1$, while the wrap-around term in the first row uses the old $x_n$. This is important for the actual iteration matrix and its convergence behavior.