Newton's Method Visualizer

\[ f(x) = x^3 - 2x + 2 \]

✓ Convergence achieved! Absolute error ≤ 1e-13

Initial Guess \( x_0 \)

Multiplicity \( m \)

Use Modified Newton's Method

Convergence Tolerance

Animation Duration (seconds per step)

Short Long

0.5 s

Current Status

Iteration: 0

Current Error: 1.00e+0

Function Value: -

\[ x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} \]

Quadratic convergence for simple roots (\(m=1\)). For roots with multiplicity \(m > 1\), linear convergence.

\[ x_{n+1} = x_n - m \cdot \frac{f(x_n)}{f'(x_n)} \]

For roots with multiplicity \(m > 1\). Restores quadratic convergence for multiple roots.

Linear: \(e_{n+1}/e_n \to \text{constant}\)

Quadratic: \(e_{n+1}/e_n^2 \to \text{constant}\)

Precision: 100-digit calculations

All code released under the MIT License.

Last modified: December 16, 2025 | High-precision calculations using Decimal.js

The Newton-Raphson Method Visualizer