Learn More
An algorithm for computing polynomial zeros, based on Aberth's method, is presented. The starting approximations are chosen by means of a suitable application of Rouché's theorem. More precisely, an integerq ≥ 1 and a set of annuliA i,i=1,...,q, in the complex plane, are determined together with the numberk i of zeros of the polynomial contained in each(More)
The relationship between univariate polynomial ∈-gcd and factorization of resultant matrices is investigated and several stable and effective algorithms for the computation of an ∈-gcd are proposed. The main result is the design of a practically stable algorithm whose arithmetic cost is quadratic in the degrees of the input polynomials. The(More)
We present the design, analysis, and implementation of an algorithm for the computation of any number of digits of the roots of a polynomial with complex coefficients. The real and the imaginary parts of the coefficients may be integer, rational, or floating point numbers represented with an arbitrary number of digits. The algorithm has been designed to(More)
Let Hn ⊂ Cn×n be the class of n × n Hessenberg matrices A which are rank-one modifications of a unitary matrix, that is, A = H + uwH , where H is unitary and u,w ∈ Cn. The class Hn includes three well-known subclasses: unitary Hessenberg matrices, companion (Frobenius) matrices, and fellow matrices. The paper presents some novel fast adaptations of the(More)