 2023

Source: Oxford Part A, A7 Numerical Analysis, A13759W1, 23 June 2023; parent PDF pages 135–137, paper pages 1–3. These original solutions cover all three questions and all eleven lettered subparts. In Question 1(d), the unrefined Gershgorin discs alone are inconclusive for the shift $5$; a further exact calculation resolves it. In Question 2(c), clearing denominators produces a linear system whose solution need not define a rational interpolant at every interpolation node. Question 3 uses the paper's normalized convention for the local truncation error.