The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x2 - N = 0. If i denotes the iteration index, the correct iterative scheme will be

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Numerical Methods

The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x² - N = 0. If i denotes the iteration index, the correct iterative scheme will be

A) $${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{i}}} + \frac{{\text{N}}}{{{{\text{x}}_{\text{i}}}}}} \right)$$ B) $${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{\text{x}}_{\text{i}}^2 + \frac{{\text{N}}}{{{\text{x}}_{\text{i}}^2}}} \right)$$ C) $${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{i}}} + \frac{{{{\text{N}}^2}}}{{{{\text{x}}_{\text{i}}}}}} \right)$$ D) $${{\text{x}}_{{\text{i}} + 1}} = \frac{1}{2}\left( {{{\text{x}}_{\text{i}}} - \frac{{\text{N}}}{{{{\text{x}}_{\text{i}}}}}} \right)$$

Answer & Solution

Correct Answer: Option A

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