Section: Engineering Mathematics | Marks: 1
The equation $g(x) = x$ is solved by Newton-Raphson iteration method, starting with an initial approximation $x_0$ near the simple root $\alpha$. If $x_{n+1}$ is the approximation to $\alpha$ at the $(n+1)^{th}$ iteration, then
- A. $x_{n+1} = \frac{x_n g'(x_n) - g(x_n)}{1 - g'(x_n)}$
- B. $x_{n+1} = \frac{x_n g'(x_n) - g(x_n)}{g'(x_n) - 1}$
- C. $x_{n+1} = g(x_n)$
- D. $x_{n+1} = \frac{x_n g'(x_n) - g(x_n) + 2x_n}{g'(x_n) + 1}$