Numerical Methods2D

Roots of Equations - Theory & Concepts - Newton Raphson

Methods for finding roots of algebraic and transcendental equations.

Finding the root of $f(x) = x^2 - 4$ using the Newton-Raphson method with initial guess $x_0 = 4$ .

Iteration Step: 0

Step 0 (Initial)Step 5

Current Guess (x_i)

4.0000

f(x_i) = 12.0000

Derivative (Slope)

8.0000

f'(x_i) = 8.0000

Formula

x_{i+1} = x_i - \frac{f(x_i)}{f'(x_i)}

x_{i+1} = 4.0000 - \frac{12.0000}{8.0000}

Next Estimate (x_i+1)

2.500000

Relative Error:Initial estimate

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