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 / iii

Table of contents
- Solution iii

Solution

The exact solution obeys

(D - L) x = Ux + b

. Subtract this from the iteration to get

(D - L) e_{n} = U e_{n - 1}

. Hence the stationary iteration matrix is

G = (D - L)^{- 1} U = (1/4 - 1/8 0 1/2) (00 - 3 0) = (00 - 3/4 3/8), e_{n} = G e_{n - 1} .

This is exactly the matrix

B

from part (a); the sign follows the given

A = D - L - U

convention.

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