conference paper published yes Michael Kerber author 36E4574A-F248-11E8-B48F-1D18A9856A870000-0002-8030-9299 Michael Sagraloff author HeEd department ISSAC: International Symposium on Symbolic and Algebraic Computation We consider the problem of approximating all real roots of a square-free polynomial f. Given isolating intervals, our algorithm refines each of them to a width at most 2-L, that is, each of the roots is approximated to L bits after the binary point. Our method provides a certified answer for arbitrary real polynomials, only requiring finite approximations of the polynomial coefficient and choosing a suitable working precision adaptively. In this way, we get a correct algorithm that is simple to implement and practically efficient. Our algorithm uses the quadratic interval refinement method; we adapt that method to be able to cope with inaccuracies when evaluating f, without sacrificing its quadratic convergence behavior. We prove a bound on the bit complexity of our algorithm in terms of degree, coefficient size and discriminant. Our bound improves previous work on integer polynomials by a factor of deg f and essentially matches best known theoretical bounds on root approximation which are obtained by very sophisticated algorithms. Springer2011California, USA eng 1104.136210.1145/1993886.1993920 209 - 216 Kerber M, Sagraloff M. 2011. Root refinement for real polynomials. ISSAC: International Symposium on Symbolic and Algebraic Computation, 209–216. Kerber, Michael, and Michael Sagraloff. <i>Root Refinement for Real Polynomials</i>. Springer, 2011, pp. 209–16, doi:<a href="https://doi.org/10.1145/1993886.1993920">10.1145/1993886.1993920</a>. Kerber M, Sagraloff M. Root refinement for real polynomials. In: Springer; 2011:209-216. doi:<a href="https://doi.org/10.1145/1993886.1993920">10.1145/1993886.1993920</a> M. Kerber and M. Sagraloff, “Root refinement for real polynomials,” presented at the ISSAC: International Symposium on Symbolic and Algebraic Computation, California, USA, 2011, pp. 209–216. M. Kerber, M. Sagraloff, in:, Springer, 2011, pp. 209–216. Kerber, Michael, and Michael Sagraloff. “Root Refinement for Real Polynomials,” 209–16. Springer, 2011. <a href="https://doi.org/10.1145/1993886.1993920">https://doi.org/10.1145/1993886.1993920</a>. Kerber, M., &#38; Sagraloff, M. (2011). Root refinement for real polynomials (pp. 209–216). Presented at the ISSAC: International Symposium on Symbolic and Algebraic Computation, California, USA: Springer. <a href="https://doi.org/10.1145/1993886.1993920">https://doi.org/10.1145/1993886.1993920</a> 33302018-12-11T12:02:43Z2021-01-12T07:42:42Z