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Numerical Methods

Quick questions on Fixed-point iteration explained: H2 Further Mathematics

3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is q1?
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State the iteration used in fixed-point iteration once the equation is in the form x=g(x)x = \mathrm{g}(x). [1 mark]
What is q2?
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What condition on g′\mathrm{g}' near a root guarantees convergence? [1 mark]
What is q3?
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If ∣g′(α)∣=1.5|\mathrm{g}'(\alpha)| = 1.5 at a root α\alpha, what happens to the iteration? [1 mark]

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