`_arb_poly_newton_convergence_factor`

Synopsis#include <flint/arb_poly.h>

void _arb_poly_newton_convergence_factor(arf_t convergence_factor, arb_srcptr poly, slong len, const arb_t convergence_interval, slong prec)

source

Sets convergence_factor to an upper bound for $C = \sup_{t, u \in I} \tfrac12 |f''(t)| / |f'(u)|$ , where $I$ is convergence_interval and $f$ is {poly, len}, obtained by evaluating $f'$ and $f''$ on $I$ . The bound is infinite unless $f'$ is bounded away from zero on $I$ ; for polynomials with large coefficients, $I$ must be narrow.

Cite this page

The FLINT team, “_arb_poly_newton_convergence_factor (arb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_poly/_arb_poly_newton_convergence_factor.html (generated 2026-11-02).

@misc{flint-doc-arb-poly-arb-poly-newton-convergence-factor,
  author       = {{The FLINT team}},
  title        = {{\_arb\_poly\_newton\_convergence\_factor (arb\_poly.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/arb_poly/_arb_poly_newton_convergence_factor.html},
  note         = {Generated 2026-11-02}
}

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