On the efficiency of some combined methods for polynomial complex zeros

摘要

Interval methods for the simultaneous inclusion of polynomial zeros produce the approximations that contain the exact zeros providing not only error bounds automatically but also take into account rounding errors without altering the fundamental structure of the interval formula. However, at present, the computational costs of most interval methods are still great, in general. In this paper several effective algorithms which preserve the inclusion property concerning the complex zeros and which have a high computational efficiency are constructed. These algorithms combine the efficiency of ordinary floating-point iterations with the accuracy control that may be obtained by the iterations in interval arithmetic. Several examples are included to illustrate the efficiency and some advantages of the proposed combined methods.