A Hybrid Method for High Precision Calculation of Polynomial Real Roots

@inproceedings{Collins1993AHM,
  title={A Hybrid Method for High Precision Calculation of Polynomial Real Roots},
  author={George E. Collins and Werner Krandick},
  booktitle={ISSAC},
  year={1993}
}
A straightforward implementation of Newton’s method for polynomial real root calculation using exact arithmetic is inefficient. In each step the length of the iterate multiplies by the degree of the polynomial while its accuracy merely doubles. We present an exact algorithm which keeps the length of each iterate proportional to its accuracy. The resulting speed-up is dramatic. The average computing time can be further reduced by trying floating point computations. Several floating point Newton… CONTINUE READING