Polynomial root finding using iterated Eigenvalue computation
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
An iterated eigenvalue algorithm for approximating roots of univariate polynomials
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
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We study the problem of approximating the zeros of an univariate polynomial (up to machine precision). Some popular iterative root-finding methods construct companion matrices (Frobenius, Lagrange) associated with the given polynomial and use eigensolvers to find the eigenvalues of such matrices. Our goal is to study this root-finding technique, exploiting the structure (e.g., diagonal plus rank one) of companion matrices to obtain a decrease of computational cost and memory requirements.