Mathematics (AS)·Numerical solutions of equations · NSSCAS 2.6.2
Iterative formulae
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In this lesson you will learn how an iterative formula written as xₙ₊₁ equals F of xₙ works like a machine that turns a rough guess into a better one, over and over, until the answer settles. You will see exactly how rearranging an equation into the form x equals F of x connects to the root you are chasing. You will build iteration tables step by step to find a root to a required accuracy, and you will learn the honest truth that some rearrangements fail to converge.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 2.6.2):
- Interpret how a given simple iterative formula xₙ₊₁ = F(xₙ) relates to the equation f(x) = 0 being solved, through the fixed-point idea x = F(x).
- Use a given iteration, or one based on a given rearrangement, to find a root to a prescribed accuracy, and understand that an iteration may fail to converge.
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