A new and novel method for computing an upper bound on the distance of an approximate zero from an exact zero of a univariate polynomial

Abstract

In this paper, we develop a simple and novel method for determining a sharp upper bound on the distance of a given approximate zero from an exact zero of a univariate polynomial. The computed bounds are scalable in the sense that we can compute sharper error bounds for better given approximations of zeros. We analyse the convergence of our method. We use requisite high precision computations for computing our bounds correctly and robustly.

Keywords:

• Error bounds
• Rouche's theorem
• A posteriori error analysis
• Approximate zeros
• High precision computation

Acknowledgement

Sudebkumar Prasant Pal acknowledges the partial support of a research grant from All India Council for Technical Education, New Delhi, India.