An algorithm for the simultaneous inclusion of real polynomial zeros

摘要

The repeated symmetric single-step (RSS) method for the simultaneous inclusion of real polynomial zeros, which is based on the symmetric single-step (SS) idea of Alefeld, is described. It is shown that the RSS method converges under the same hypotheses as the total-step (T) and single-step (S) methods. Computational results indicate that RSS is more efficient than T, S, and SS for bounding the real zeros of real polynomials, and preliminary experiments with complex rectangular interval arithmetic [8, 9] suggest that the same is true for complex polynomial zeros.