A modified companion matrix method based on Newton polynomials
Daniela Calvetti, Lothar Reichel, Fiorella Sgallari · Contemporary mathematics - American Mathematical Society · 2003
One of the most popular methods for computing the zeros of a polynomial in power form is to determine the eigenvalues of the associated companion matrix. This approach, which commonly is referred to as the companion matrix method, however, can yield poor accuracy. We demonstrate that when approximations of the zeros are available, their accuracy often can be improved by computing the eigenvalues of a modi ed companion matrix associated with the polynomial expressed in a basis of Newton polynomials de ned by the available approximations of the zeros. The latter approximations can be determined in many ways, e.g., by the companion matrix method.