Abstract by Zach Taylor
A New Matrix Based Method for Computing Univariate Polynomial Roots
A traditional approach to finding the roots of a univariate polynomial is to construct the companion matrix for that polynomial and calculate its eigenvalues. We present here a similar method using the inverse of the companion matrix and show how it can improve the numerical stability of calculating the roots in some cases. We also present an analoge for this matrix in terms of the Chebyshev polynomial basis and discuss its advantages over the usual companion matrix.