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Establish iteration formula to find the
reciprocal of a positive number N by N-R method?
Answers
Step-by-step explanation:
The iterative sequence of newton raphson method to find the value of the reciprocal of positive no. N is given by
Answer: x(n) = 2x(n-1) - Nx²(n-1), where n≥1, x(0) is the initial approximation.
Step-by-step explanation: Hi, ...
x(n) = 2x(n-1) - Nx²(n-1), where n≥1. x(0) is the initial approximation.
Hope, it helps !
Given : reciprocal of a positive number N
Newton raphson Method
To Find : Establish an iteration
Solution:
x = 1/N
=> 1/x = N
f(x) = 1/x - N
f'(x) = -1/x²
xₙ₊₁ = xₙ − f(xₙ) / f'(xₙ)
x₁ = x₀ - f(x₀)/f'(x₀)
=> x₁ = x₀ - (1/x₀ - N)/(-1/x₀²)
=> x₁ = x₀ + x₀²(1/x₀ - N)
=> x₁ = x₀ + x₀ - x₀² N
=> x₁ = 2x₀ - x₀² N
x₂ = x₁ - f(x₁)/f'(x₁)
=> x₂ = x₁ - (1/x₁ - N)/(-1/x₁²)
=> x₂ = x₁ + x₁ - x₁²N
=> x₂ = 2x₁ - x₁²N
xₙ₊₁ = 2xₙ - xₙ²N
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