Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability / 5 / b / i

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- Solution i

Solution

The Newton root-finding iteration is

x_{k + 1} = x_{k} - \frac{x _{k}^{6} - 5 x _{k}^{4} + 6}{6 x _{k}^{5} - 20 x _{k}^{3}} .

It is defined when

x_{k} \in / {0, \pm 10/3}

. Finding an exact zero of a function is a stopping condition, rather than a reason to continue dividing.

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