butiran

newton-raphson method

intro

The Newton-Raphson method is a method for finding succesively and quickly better approximation for the roots of a real-valued functions (Çapar, 2020). It is one of the most widely used methods for root finding and it can be shown that this technique is quadratically convergent as the root aproached (Smith, 1998). This algorithm is quite versatile with wide-ranging use cases than span many domains, e.g by reframing the function of interest for the value of $x$ that yields a certain value rather than being restricted to $0$ can be searched (Dolphin, 2022). There is a report about historical development of this method (Ypma, 1995), where there are differences between this technique and Newton’s technique (Nadhim & Al-Jilawi, 2022).

formula

flowchart

algorithm

  1. Start.
  2. Input $f(x)$, $f’(x)$, $\varepsilon$, $x_0$.
  3. Set $n = 0$.
  4. Calculate $x_{n+1} = x_n - f(x_n) / f’(x_n)$.
  5. If $f(x_{n+1}) < \varepsilon$, go to Step 8.
  6. Increase $n$ using $n = n + 1$.
  7. Go to Step 4.
  8. Print $x_{n+1}$.
  9. End.

problem

code

graphics

challenges

refs