Methods of Search for Solving Polynomial Equations

摘要

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 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 non-optimality of certain methods, both on a deterministic and on a probabilistic basis, are established. (Author)