The <power method> repeatedly normalizes $Aq^{(k)}$ and estimates the <eigenvalue> with the Rayleigh quotient $(q^{(k)})^TAq^{(k)}$. It converges when the <dominant eigenvalue> is unique in <modulus> and the initial <vector> has a nonzero component in its eigendirection.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 41B / a / Solution

 Solution (source code)