Horner's Method
The video covering Horner's Method with Ruffini's Rule can be found at https://youtu.be/zEvfkSuPqWk. Example code is given in Horner.jl file, written in Julia it has Horner's Method and Ruffini's Rule with derivatives for finding roots of polynomials. You can run the program online from CodingGround. To run the program locally have Julia installed (julialang.org/) then type julia Horner.jlin the terminal in the directory where Horner.jl is saved. If you'd rather not use the terminal, use an IDE instead like Geany to run the program (change the execute option to Julia %e.jl). This method is also used in Durand-Kerner and Aberth-Ehrlich documented here.
To change the polynomial being solved update the coefficients stored here p = [-2310, 727, 382, -72, -8, 1] meaning x5 - 8x4 - 72x3 + 382x2 + 727x - 2310.
Reference links:
- Horner's paper https://www.jstor.org/stable/107508
- Ruffini https://doi.org/10.1090/S0002-9904-1911-02072-9
- Chemla's paper https://doi.org/10.1017/S0957423900001235
- Qin Jiushao http://citeseerx.ist.psu.edu/
- Sharaf al-Dīn al-Tūsī https://doi.org/10.1016/0315-0860(89)90099-2
- Jia Xian https://www.math.vt.edu/people/brown/doc/fibo_number.pdf
- Yong's paper https://sms.math.nus.edu.sg