numerical-veliz

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numerical-veliz

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Numerical Analysis code from the Oscar Veliz YouTube Channel

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- - bug_report.md
  - topic-request.md
- CODE_OF_CONDUCT.md
- CONTRIBUTING.md
- FUNDING.yml
- PULL_REQUEST_TEMPLATE.md
- SUPPORT.md
- 404.md
- _config.yml
- CNAME
- index.md
- - x3m1.png
  - x4p1.png
  - x8p15x4m16.png
- - z3-1.png
  - z3-1square.png
  - z8+15z4-15.png
- - arctan-half.png
  - arctan-halfhalfi.png
  - arctan-square.png
  - arctan.png
  - sin-half.png
  - sin-halfhalfi.png
  - sin-zoom.png
  - sin-zoom2.png
  - sin.png
  - z3-1(color).png
  - z3-1.png
  - z3-1half.png
  - z3-1halfhalfi.png
  - z8+15z4-16(color).png
  - z8+15z4-16.png
  - z8+15z4-16half.png
  - z8+15z4-16halfhalfi.png
  - z8+15z4-16halfhalfizoom.png
- - arctan.svg
  - arctan_interval.svg
  - x^2-x-1.svg
  - x^3-x^2-x-1.svg
- - arctan.png
  - arctanhalf.png
  - arctanhalfhalfi.png
  - sinz.png
  - sinzhalf.png
  - sinzhalfhalfi.png
  - z3-1.png
  - z3-1color.png
  - z3-1half.png
  - z3-1halfhalfi.png
  - z8+15z4-16.png
  - z8+15z4-16color.png
  - z8+15z4-16half.png
  - z8+15z4-16halfhalfi.png
  - z8+15z4-16zoom0001.png
  - z8+15z4-16zoom001.png
  - z8+15z4-16zoom01.png
  - z8+15z4-16zoom1.png
- - -cos.png
  - -cos_zoom14.png
  - arctan.png
  - z4o4-z.png
  - z4o4-zcolor.png
  - z4o4-zhalf+halfi.png
  - z4o4-zhalf+halfizoom.png
  - z9o9+3z5-16z-full.png
  - z9o9+3z5-16z.png
  - z9o9+3z5-16zhalfhalfi.png
  - z9o9+3z5-16zhalfhalfizoom52.png
- - z3-1.png
  - z8p15z4-16.png
- - z3-1(color).png
  - z3-1.png
  - z3-1half.png
  - z3-1halfhalfi.png
  - z8+15z4-16(colored).png
  - z8+15z4-16(zoom).png
  - z8+15z4-16.png
  - z8+15z4-16half.png
  - z8+15z4-16halfhalfi.png
- - circleparabola-color.png
  - circleparabola-halfhalfi.png
  - circleparabola.png
  - global1.svg
  - global2.svg
  - newton1.svg
  - newton2.svg
  - phiphi-color.png
  - phiphi-halfhalfi.png
  - phiphi.png
- - arctan-half.png
  - arctan-halfhalfi.png
  - arctan.png
  - basic-converge1.png
  - globalz2+1.png
  - globalz3-1.png
  - globalz3-1div2i.png
  - sin-half.png
  - sin-halfhalfi.png
  - sin1.png
  - sin2.png
  - sin3.png
  - z8+15z4-16halfhalfi.png
  - z8-1.png
  - z8-2.png
  - zcube-extra1.png
  - zcube-extra2.png
  - zcube1.png
  - zcube2.png
  - zcube3.png
  - zcube4.png
  - zcube5.png
  - zcube6.png
  - zcube7.png
  - zcube8.png
- - basic_interval.svg
  - newton_converge.svg
  - newton_diverge.svg
  - wide_newton.svg
- - 2atantanhxo2.svg
  - asecsqrt2exp.svg
  - atan.svg
  - logsec.svg
  - logtanxo2ppio4.svg
  - sec.svg
  - tan.svg
- - PowerMethod.ml
- - BrentJarratt.fsx
  - JarrattFractal.plt
  - TernDichFibGold.pas
- - Bairstow.py
  - Bernoulli.jl
  - BrentDekker.hs
  - ComplexRoots.plt
  - FalsePosition.c
  - GlobalNewtonFractal.plt
  - Graeffe.m
  - HalleyFractal.plt
  - Horner.jl
  - Householder.m
  - HouseholderFractal.plt
  - JenkinsTraub.py
  - Laguerre.pl
  - LaguerreFractal.plt
  - LehmerSchur.py
  - Muller.py
  - NewtonFractal.plt
  - NewtSafe.adb
  - PlotNewtonHalley.r
  - Steffensen.sml
  - Taylor.m
  - Wegstein.kt
  - wilf.py
- - e-spigot.py
  - Machin.lsp
  - Sublinear.py
  - Taylor.m
- - DurandKernerAberthEhrlich.go
  - FixedPointAitkenSteffensen.rs
  - GeneralHalley.m
  - GeneralizedBisection.py
  - GeneralNewton.m
  - GlobalNewtonFractal.jl
  - MultiNewtonFractal.plt
  - QuasiNewton.jl
LICENSE
README.md

// repository documentation

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# numerical-veliz

[![MIT license](http://img.shields.io/badge/license-MIT-brightgreen.svg)](http://opensource.org/licenses/MIT) ![GitHub last commit](https://img.shields.io/github/last-commit/osveliz/numerical-veliz) ![GitHub code size in bytes](https://img.shields.io/github/languages/code-size/osveliz/numerical-veliz) ![GitHub language count](https://img.shields.io/github/languages/count/osveliz/numerical-veliz) ![GitHub top language](https://img.shields.io/github/languages/top/osveliz/numerical-veliz) ![GitHub followers](https://img.shields.io/github/followers/osveliz?style=social) ![GitHub User's stars](https://img.shields.io/github/stars/osveliz?style=social)

Example code from the Oscar Veliz YouTube channel <https://www.youtube.com/OscarVeliz>.
This repo contains methods for finding roots, minimizing functions, solving systems of equations, and many other numerical algorithms!
See the [Wiki](https://github.com/osveliz/numerical-veliz/wiki) for more documentation.
Become a [GitHub Sponsor](https://github.com/sponsors/osveliz) to support this project!
For community guidelines visit the [Code of Conduct](/.github/CODE_OF_CONDUCT.md) and [Contributing](/.github/CONTRIBUTING.md) documents.
Bug Reports and Topic Requests can be made submitted in the [Issues](https://github.com/osveliz/numerical-veliz/issues) forum.
Distributed under MIT License.

## Newton Fractals generated in gnuplot using [NewtonFractal.plt](https://github.com/osveliz/numerical-veliz/tree/master/src/rootfinding/NewtonFractal.plt)

![z^3](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/NewtonFractal/zcube1.png)
![rgb](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/NewtonFractal/z3/RGB.png)
![generalized z^3](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/NewtonFractal/zcube8.png)
![z^8-15z^4+16](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/NewtonFractal/z8-1.png)
![z^8 colored](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/NewtonFractal/z8/z8.png)
![sinz(z)](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/NewtonFractal/sin3.png)

## Halley Fractals generated in gnuplot using [HalleyFractal.plt](https://github.com/osveliz/numerical-veliz/tree/master/src/rootfinding/HalleyFractal.plt)

![z^3](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/HalleyFractal/z3-1.png)
![z^3](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/HalleyFractal/z3-1(color).png)
![z^8](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/HalleyFractal/z8+15z4-16.png)
![z^8](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/HalleyFractal/z8+15z4-16(color).png)
![zoom](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/HalleyFractal/z8+15z4-16halfhalfizoom.png)

## Householder Fractals generated in gnuplot using [HouseholderFractal.plt](https://github.com/osveliz/numerical-veliz/tree/master/src/rootfinding/HouseholderFractal.plt)

![z^3](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/HouseholderFractal/z3-1.png)
![z^3](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/HouseholderFractal/z3-1color.png)
![z^8](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/HouseholderFractal/z8+15z4-16.png)
![z^8](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/HouseholderFractal/z8+15z4-16color.png)
![zoom](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/HouseholderFractal/z8+15z4-16zoom0001.png)

## Laguerre Fractals generated in gnuplot using [LaguerreFractal.plt](https://github.com/osveliz/numerical-veliz/tree/master/src/rootfinding/LaguerreFractal.plt)

![z^3-1](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/LaguerreFractal/z3-1halfhalfi.png)
![z^3-1color](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/LaguerreFractal/z3-1(color).png)
![z^8+15z^4-16](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/LaguerreFractal/z8+15z4-16.png)
![z^8+15z^4-16general](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/LaguerreFractal/z8+15z4-16halfhalfi.png)
![z^8+15z^4-16zoom](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/LaguerreFractal/z8+15z4-16(zoom).png)
![z^8+15z^4-16color](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/LaguerreFractal/z8+15z4-16(colored).png)

## Newton's Method visualizations created using [PlotNewtonHalley.r](https://github.com/osveliz/numerical-veliz/tree/master/src/rootfinding/PlotNewtonHalley.r)

![interval](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/NewtonInterval/basic_interval.svg)
![converging](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/NewtonInterval/newton_converge.svg)
![diverging](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/NewtonInterval/newton_diverge.svg)
![newton_gamma](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/NewtonInterval/wide_newton.svg)

## Halley's Method created using [PlotNewtonHalley.r](https://github.com/osveliz/numerical-veliz/tree/master/src/rootfinding/PlotNewtonHalley.r)

![arctan](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/HalleyPlot/arctan.svg)
![psi](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/HalleyPlot/x^2-x-1.svg)
![trib](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/HalleyPlot/x^3-x^2-x-1.svg)

## Taylor Series created using [Taylor.m](https://github.com/osveliz/numerical-veliz/tree/master/src/series/Taylor.m)

![arctan](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/TaylorSeries/atan.svg)
![sec](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/TaylorSeries/sec.svg)
![logtan](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/TaylorSeries/logtanxo2ppio4.svg)

## Complex Plots created using [ComplexRoots.plt](https://github.com/osveliz/numerical-veliz/blob/master/src/rootfinding/ComplexRoots.plt)

![z3-1](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/ComplexRoots/z3-1.png)
![z^8+15z^4-16](https://raw.githubusercontent.com/osveliz/numerical-veliz/master/photos/ComplexRoots/z8%2B15z4-15.png)

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