 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2017/digital-systems-linear-algebra-introduction-to-formal-proof/6/b/i/solution

The Gauss-Seidel method solves each component using the already updated components from the same iteration. In the splitting

A = D - L - U

, those updated diagonal and lower-triangular terms stay on the left, while upper-triangular terms use the previous iterate. Thus

(D - L) x_{n} = U x_{n - 1} + b .

Here

D - L

is lower triangular with nonzero diagonal, so each new iterate is obtained by forward substitution, starting from the specified zero vector.

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