Calculus & Numerical Methods
Fixed-Point Iteration
Iterate x = g(x) from a starting value.
Formula
Formula
xn+1 = g(xn)
Variables
| Symbol | Definition | Type & range | Units | Role |
|---|---|---|---|---|
| g | iteration function | expression / text | x | input |
| x₀ | start | computed result | — | result |
| n | iterations | integer (ℤ) | — | input |
Try it yourself
Interactive calculator
Worked examples
Example 1
Giveng(x) = (x + 2/x)/2, x₀ = 1, iterations = 50
Result1.414213562
Example 2
Giveng(x) = cos(x), x₀ = 1, iterations = 80
Result0.7390851332