{"day":"08","month":"06","status":"public","year":"2011","scopus_import":1,"main_file_link":[{"url":"http://arxiv.org/abs/1104.1362","open_access":"1"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","publication_status":"published","language":[{"iso":"eng"}],"department":[{"_id":"HeEd"}],"oa":1,"doi":"10.1145/1993886.1993920","external_id":{"arxiv":["1104.1362"]},"date_created":"2018-12-11T12:02:43Z","page":"209 - 216","abstract":[{"text":"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.","lang":"eng"}],"author":[{"last_name":"Kerber","orcid":"0000-0002-8030-9299","first_name":"Michael","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","full_name":"Kerber, Michael"},{"full_name":"Sagraloff, Michael","first_name":"Michael","last_name":"Sagraloff"}],"conference":{"end_date":"2011-06-11","name":"ISSAC: International Symposium on Symbolic and Algebraic Computation","start_date":"2011-06-08","location":"California, USA"},"oa_version":"Preprint","arxiv":1,"citation":{"ama":"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>","ista":"Kerber M, Sagraloff M. 2011. Root refinement for real polynomials. ISSAC: International Symposium on Symbolic and Algebraic Computation, 209–216.","ieee":"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.","apa":"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>","mla":"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>.","short":"M. Kerber, M. Sagraloff, in:, Springer, 2011, pp. 209–216.","chicago":"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>."},"publisher":"Springer","_id":"3330","type":"conference","publist_id":"3304","date_published":"2011-06-08T00:00:00Z","title":"Root refinement for real polynomials","quality_controlled":"1","date_updated":"2021-01-12T07:42:42Z"}