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I am currently writing a program in TI-BASIC to compute the eigenvalues and associated eigenvectors of a given matrix (I am working with a TI83 Premium CE that doesn't offer such a program). I have found and written an algorithm to compute the coefficients of the characteristic polynomial of the given matrix (using Le Verrier algorithm). So I want to implement a root-finding algorithm to compute the matrix's eigenvalues. I found several methods in this article : https://en.wikipedia.org/wiki/Root-finding_algorithms (especially in the polynomial section). I found here the source code for plysmlt2, the program implemented by default to find root of polynomial but I can't open it because of the format. It was written in assembly code.

Is there a simple (= efficent, not too memory-consuming) root finding method to find all root of a given polynomial ?

I am searching for a method that converges almost certainly (the Newton-method is good but not robust in my case).

Edit: I'm interested in real AND complex roots

Marco Bonelli
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Elyo
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    You should specify whether you're only interested in real roots or also complex roots. – orlp Nov 27 '21 at 22:49
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    https://math.stackexchange.com/questions/44977/ti-83-plus-is-it-possible-to-find-the-eigenvalues-on-this-calculator – maraca Nov 28 '21 at 03:23
  • @orlp thank you, I edited my post. I want to find both real and complex roots, but in my field, the roots are likely to be real. – Elyo Nov 28 '21 at 10:39

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