fixed-point iteration
What fixed-point iteration means in Mathematics A-Level, as defined for Pearson Edexcel, WJEC.
Definitions of fixed-point iteration
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Reference: Pearson Edexcel
Rearranging an equation f(x) = 0 into the form x = g(x), then choosing a starting value x₀ and computing x₁ = g(x₀), x₂ = g(x₁), and continuing.
Rearranging f(x) = 0 into the fixed-point form x = g(x) and generating the recurrence relation xₙ₊₁ = g(xₙ) from an initial approximation x₁.
Rearranges f(x) = 0 into x = g(x), chooses x₁, then iterates to solve other recurrence relations xₙ₊₁ = g(xₙ).
Topics that use fixed-point iteration
- Numerical methods (Pearson Edexcel A-Level)
- Numerical Methods (A2 Unit 3: Pure Mathematics B) (WJEC A-Level)
Related terms
- cobweb diagram
- divergence
- Newton-Raphson method
- staircase diagram
- Trapezium rule
- Bisection and interval narrowing
- bounds for the true integral
- change of sign
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