Correct Answer - Option 4 : Stationary
Concept:
Newton-Raphson Method:
The iteration formula is given by
\({x_{n + 1}} = {x_n} - \frac{{f\left( {{x_n}} \right)}}{{f'\left( {{x_n}} \right)}}\)
Where x0 is the approximate root of the equation f(x) = 0
Important Points:
- Newton’s method is useful in cases of large values of f’(x) i.e. when the graph of f(x) while crossing the x-axis is nearly vertical.
- It is not preferred when the graph of f(x) is nearly horizontal where it crosses the x-axis as the values of f’(x) have negative values in this case.
- It is sensitive to starting value. Convergence fails if the starting point is nor near the root.
- The formula converges provided the initial approximation x0 is chosen sufficiently close to the root.
- It is generally used to improve the result obtained by the other methods.
- It has quadratic convergence i.e. order of convergence is 2. The subsequent error at each step is proportional to the square of the error at the previous step.
Explanation:
The points where the function f(x) approaches infinity are called as Stationary points. At stationary points, Newton Raphson fails and hence it remains undefined for Stationary points.
