_acb_poly_find_roots_double
#include <flint/acb_poly.h>double _acb_poly_find_roots_double(acb_ptr roots, acb_srcptr poly, acb_srcptr initial, slong len, slong maxiter, slong prec)sourceSets {roots, len - 1} to approximations of the roots of {poly, len} computed by cd_poly_find_roots in double precision after rescaling x and the coefficients so that the coefficients are representable as doubles, with the radii set to zero. Returns the largest relative step of the last iteration. prec (if below 53) only serves as an early termination criterion.
The scaling factors are chosen as the line that best fits the points (i, \log_2 |a_i|) in the minimax sense, computed with the convex hulls of these points. Barring overflow and up to rounding errors, the Gershgorin circle theorem places the roots in the union of the disks centred at the outputs z_k with radius (\mathit{len} - 2) |z_k| times the returned correction.
The FLINT team, “_acb_poly_find_roots_double (acb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_poly/_acb_poly_find_roots_double.html (generated 2026-10-20).
@misc{flint-doc-acb-poly-acb-poly-find-roots-double,
author = {{The FLINT team}},
title = {{\_acb\_poly\_find\_roots\_double (acb\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_poly/_acb_poly_find_roots_double.html},
note = {Generated 2026-10-20}
}