From: Raymond T. <toy...@gm...> - 2014-07-08 16:21:43
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>>>>> "Stavros" == Stavros Macrakis <(Σταῦρος Μακράκης)" <mac...@al...>> writes: Stavros> Understood that this is not a solved problem. However, it Stavros> would be useful to give users who aren't familiar with Stavros> Jenkins-Traub some guidance. The paper is available online at http://www.jstor.org/stable/2949376. It only says that the algorithm always converges (mathematically). A peek at the original Fortran code indicates that the algorithm converges when the polynomial value is smaller than a bound on the error in evaluating the polynomial. Stavros> I was also surprised that sols:allroots(eq:x^243+23*x-24) gives a warning: Stavros> allroots: Stavros> unexpected error; treat results with Stavros> caution. Stavros> allroots: Stavros> only 65 out of 243 roots found. Stavros> and the first element of the result list is a reduced polynomial. Stavros> This behavior isn't warned against in the doc at all. Oops. Yeah, that should be documented. Curiously, bfallroots finds all 243 roots even with fpprec = 16. Comparing with the roots with fpprec=100 shows that only the first 13 or so are correct. (I didn't check that roots were produced in the same order.) Ray |