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

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