A method for finding the zeros of polynomials using a companion matrix.
In this paper the problem of finding zeros of a monic polynomial of degree \(n\) is transformed to the problem of finding eigenvalues of the corresponding companion matrix. A new method is presented by constructing a new companion matrix which has only simple eigenvalues. All the distinct zeros of a polynomial and their multiplicities can be calculated by this method.
scientific article; zbMATH DE number 2032557