alan2here
commented
2 years ago There's also a way to solve polynomials with physics by using a few mirrors affixed at right angles and a laser.
Open osveliz opened 2 years ago
alan2here
commented
2 years ago There's also a way to solve polynomials with physics by using a few mirrors affixed at right angles and a laser.
Portfolio
I made a video on a polynomial root solver known as Aberth-Ehrlich which finds all of the zeros simultaneously.
Aberth and Ehrlich separately derived the method below in two different ways:
$$ X{n+1}^{(i)} = X{n}^{(i)} - { {p(X{n}^{(i)}) \over p'(X{n}^{(i)})} \over 1 - {p(X{n}^{(i)}) \over p'(X{n}^{(i)})} \Sigma{j = 1, j \neq i}^n {1 \over {X{n}^{(i)} - X_{n}^{(j)} } } } $$
Ehrlich used Newton's Method $$ x_{n+1} = x_n - {p(x_n) \over p'(x_n)} $$
Aberth used Vector Fields and Electrostatics which I have very little understanding of. I would love to make a video describing Aberth's approach, showing how Physics can be used to solve polynomials and I need help from a domain expert with knowledge of Vector Fields and/or Electrostatics.
Please watch my video to see how it was derived with Newton's Method and Newton Fractals. I have example code written in GoLang which you can find on my repo here or run online via TutorialsPoint.
Target topic categories
Numerical Analysis Physics Electrostatics Vector Fields Numerical Methods Newton's Method Newton Fractals
Target medium
Video
Contact details
You can find me on my YouTube channel or send an email to oscar@oveliz.com
Additional context
As a different search, I would love to find someone who could make really amazing animations of charged particles and vector fields but that can wait.
For additional background, some familiarity with Newton Fractals could be helpful. You can watch my old video or the new ones from 3b1b.
It could also be helpful to be familiar with Durand-Kerner, a method similar to and simpler than Aberth-Erhlich, which I also have a video on.
My repo distributes under MIT licensing.