Methods of Search for Solving Polynomial Equations
Peter Henrici · Journal of the ACM · 1970
The problem of determining a zero of a given polynomial with guaranteed error bounds, using an amount of work that can be estimated a priori, is attacked here by means of a class of algorithms based on the idea of systematic search.Lehmer's "machine method" for solving polynomial equations is a special case.The use of the Schur-Cohn algorithm in Lehmer's method is replaced by a more general proximity test which reacts positively if applied at a point close to a zero of a polynomial.Various such tests are described, and the work involved in their use is estimated.The optimality and nonoptimality of certain methods, both on a deterministic and on a probabilistic basis, are established.