We show that it is always possible to transform the problem of finding the roots of a generic polynomial to the problem of determining the eigenvalues of tridiagonal matrices having only simple eigenvalues. Since this problem is very efficiently solved, for example with the familiar QR method, it seems that the present very simple approach has the potentiality to supplant the existing ones. © 1995.
Brugnano, L., & Trigiante, D. (1995). Polynomial roots: The ultimate answer? Linear Algebra and Its Applications, 225(C), 207–219. https://doi.org/10.1016/0024-3795(93)00341-V