COMPLEX-COEFFICIENT POLYNOMIAL ROOTS BY A STABILITY CRITERION

Abstract

Abstract. Computation of polynomial roots is a problem that arises in various domains of science and engineering, and has thus received much attention in years, with marked recent progress. This paper introduces a new numerical algorithm for computing the roots of a complex-coefficient polynomial of degree n. The method is based on bracketing, in the spirit of Lehmer-Schur [1], but uses a robust stability criterion from system theory due to Agashe [2], which generalizes the Routh-Hurwitz criterion. The algorithm is simple to implement, and its accuracy is tested using both well- and ill-conditioned polynomials. The results show excellent convergence, as compared to the companion-matrix eigenvalues method used often in numerical packages, such as MATLAB [3]. The algorithm is also flexible: precision can be tuned, and custom search regions can be specified. Key Words. Polynomial, root, algorithm, bracketing and stability. 1