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Graeffe's Method

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Oscar Veliz edited this page Jun 6, 2022 · 7 revisions

Graeffe's Method video

The video covering Graeffe's Method (also called Graeffe-Dandelin-Lobachevskiĭ or Dandelin–Lobachesky–Graeffe method) can be found at https://youtu.be/92oh5gYUP7Y. Example code is given in Graeffe.m file, written in GNU Octave. You can run the program online from Octave-Online (although it might time out). To run the program locally have Octave installed (https://www.gnu.org/software/octave/) then type octave Graeffe.m in the terminal in the directory where Graeffe.m is saved or run it from within the Octave application by typing the command source("Graeffe.m").

Special Installation Instructions

You may also need to install Python and SymPy which can be done by running the command pip install sympy once Python is installed. Then from within Octave install the symbolic package using the command pkg install -forge symbolic. To check that it installed correctly run the command pkg load symbolic. You should only need to install SymPy and the symbolic package once.

Example Polynomials

You can replace the given polynomial f = x^3 - 13*x^2 + 32*x - 20 with your desired polynomial. Here are some additional examples:

Graeffe's example polynomial

f = x^4 - 14*x^3 + 59*x^2 - 94*x + 48

Dandelin's example polynomial

f = expand((x-100)*(x-1)*(x-1/100))

Lobachevskiĭ's example polynomial

f = x^5 - 3*x^4 - 7*x^3 - 5*x^2 + 1

Wilkinson Polynomial (x-1)(x-2)...(x-20), considering lowering stopping epsilon otherwise it will take some time

f = wilkinson()

Reference links:

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