The Newton-Raphson iteration can be used to compute the.
2008
The Newton-Raphson iteration
can be used to compute the.
- A.
square root of R
- B.
logarithm of R
- C.
reciprocal of R
- D.
square of R
Show answer & explanation
Correct answer: A
The given iteration is
xₙ₊₁ = 1/2 (xₙ + R/xₙ).
This is obtained by applying Newton-Raphson method to the equation
f(x) = x² - R = 0.
For f(x) = x² - R, we have f'(x) = 2x.
Newton-Raphson gives
xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ)
= xₙ - (xₙ² - R)/(2xₙ)
= (1/2)(xₙ + R/xₙ).
The root of x² - R = 0 is x = √R, so the iteration computes the square root of R.