Householder's Method
The video covering Householder's Method can be found at https://youtu.be/F9DFewL0mho. Example code is given in Householder.m file, written in GNU Octave. You can run the program online from CodingGround or Octave-Online (although it might time out). To run the program locally have Octave installed (https://www.gnu.org/software/octave/) then type octave --no-gui Householder.m in the terminal in the directory where Householder.m is saved or run it from within the Octave application by typing the command source("Householder.m").
To change the function being solved update the instruction func = "x^8 + 15*x^4 - 16" to any desired function (represented as a string). For Householder Fractal documentation visit here.
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.
Reference links:
- Householder's book https://archive.org/details/principlesofnume030218mbp/page/n143
- Petković's paper https://www.sciencedirect.com/science/article/pii/S0377042709006347