Abstract
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 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.
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