Project ForgeEngineering Mathematics
Numerical Methods
GATE 2008
Easy
The Newton-Raphson iteration x_(n+1) = (1/2)(x_n + R/x_n) can be used to compute the:
- Asquare of R
- Breciprocal of R
- square root of R
- Dlogarithm of R
Explanation
This is exactly the Newton-Raphson iteration for finding a root of f(x) = x² − R (i.e. x_(n+1) = x_n − f(x_n)/f'(x_n) = x_n − (x_n²−R)/(2x_n) = (x_n + R/x_n)/2), so it converges to √R.
Source: GATE CS 2008 (2008)
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