What is the Newton-Raphson Method?
The Newton-Raphson Method is an efficient numerical method for finding successively better approximations to the roots (or zeroes) of a real-valued function. It uses the derivative of the function for more accurate results.
What is the Newton-Raphson Method?
The Newton-Raphson Method is an efficient numerical method for finding successively better approximations to the roots (or zeroes) of a real-valued function. It uses the derivative of the function for more accurate results.
Learn more about how it works
- Start with an initial guess \(x_0\).
- Use the formula \(x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}\) to find the next approximation.
- Repeat the process until the result converges (when \(f(x)\) is sufficiently close to zero).
- The derivative \(f'(x)\) is essential for the method to work, and if \(f'(x)\) is too small, the method may fail.
Input Parameters
Try these:
x³ - 2x - 5
x² - 4
log(x) - 2
e^x - 3
x⁴ - 16
cos(x) - x
x³ + 4x² - 10
Steps & Output
| Iteration | x | f(x) | f'(x) |
|---|