The Order of Convergence of Newton Raphson Method is?

By BYJU'S Exam Prep

Updated on: November 9th, 2023

The Order of Convergence of Newton Raphson Method is 2. One of the most popular methods for determining the roots of given equations is the Newton-Raphson Method. To solve a system of equations, it can be generalized effectively. Furthermore, we can demonstrate that the procedure is quadratically convergent as we get closer to the root.

Order of Convergence of Newton Raphson Method

One of the quickest techniques among the fake position and bisection techniques is the Newton-Raphson Method. Take one initial approximation in this method rather than two. It is the procedure for finding the true root of an equation with the form f(x) = 0, given merely one point that is close to the desired root.

The Newton-Raphson method converges with an order of 2 or quadratic convergence. If |f(x).f’’(x)| < |f’(x)|2, it converges. Also, if f'(x) = 0, this technique fails. Newton’s approach is founded on the idea that when you zoom in close enough to a function, continuous derivative functions like straight lines.

  • Newton’s Method has a straightforward and user-friendly algorithm.
  • It is based on the fundamental calculus idea that the slope of the line tangent to the graph of y=f(x) at the point (c,f(c)) is the derivative of a function f at x=c.
  • Newton Raphson Method method employs the first derivative of a function.


The Order of Convergence of Newton Raphson Method is?

For Newton Raphson Method, the order of convergence is 2. Newton’s method involves two evaluations of the function and its derivative for each iteration. The convergence speed is actually 2-order since the derivative is frequently as expensive to assess as the integral (and frequently more), resulting in two evaluations for each iteration.

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