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Newton's Method

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Oscar Veliz edited this page Nov 26, 2021 · 11 revisions

A playlist of all videos related to Newton's Method can be found here.

Roots of a Function

Newton's Method video Video Mistakes Interval of Convergence Newton-Bisection Hybrid Newton Fractal

There are multiple videos related to Newton's Method for finding the root of a single equation. The Original and the Video Mistakes. The topic is also expanded upon in Newton's Method Convergence Interval (code: here documentation: here) and Newton-Bisection Hybrid (code: here documentation: here) as well as Newton Fractals (code: here documentation: here).

Solving Systems of Equations

Generalized Newton's Method video

Solving nonlinear systems with Generalized Newton's Method is discussed in this video with code located in Generalized Newton's Method. It is written in GNU Octave but should work in MATLAB. To run locally use the command octave GeneralNewton.m. The code can be run online through octave-online. If locally using GNU Octave, be sure that the symbolic package has been installed. In case it isn't use the command pkg install -forge symbolic which only has to be run once. Documentation for the symbolic package can be found here. Multivariable Fractal information can be found here.

References

Global Newton's Method

Global Newton's Method video

Globally convergent newton's method for a single equation, as well as nonlinear systems, to always find a solution (although the solution might be a minimum). Video can be found here with single equation fractal code here and nonlinear system fractal code here. Visit Newton Fractal page for additional documentation.

References

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