Newton's method done right

Version 1.3 (137 KB) by Andrew Knyazev
Newton's method for solving systems of nonlinear equations, including nonsquare and inconsistent
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Updated 9 Dec 2025

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Newton's method for solving a system of nonlinear equations, see http://en.wikipedia.org/wiki/Newton's_method
Newton(X,F,X0) solves nonlinear system F(x)=0 by Newton's method, using the given initial approximation X0. The derivative (Jacobian) is evaluated symbolically. The iterations are performed numerically.
The included demo NewtonDemoRunMe.m shows how to run the Newton.m function. E.g., it creates a slide-show and a movie, illustrating the behavior of the iterates.

Cite As

Andrew Knyazev (2026). Newton's method done right (https://in.mathworks.com/matlabcentral/fileexchange/33672-newton-s-method-done-right), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2025b
Compatible with any release
Platform Compatibility
Windows macOS Linux
Categories
Find more on Systems of Nonlinear Equations in Help Center and MATLAB Answers
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Acknowledgements

Inspired: GUI for "Newton's Method Done Right"

Version Published Release Notes
1.3

Light editing.
The demo updated to make movies in the latest MATLAB and now uses the color‑blind–friendly palette Okabe–Ito.
1.2

Multiple improvements and updates.
added a conversion to a toolbox
1.1.0.0

Bug fixes in Newton.m and a new script NewtonDemoRunMe.m with examples.

1.0.0.0