English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Evaluating or finding the roots of a polynomial $f(z) = f_0 + \cdots + f_dz^d$ with floating-point number coefficients is a ubiquitous problem. By usinga piecewise approximation of $f$ obtained with a careful use of the Newtonpolygon of $f$, we improve state-of-the-art upper bounds on the number ofoperations to evaluate and find the roots of a polynomial. In particular, ifthe coefficients of $f$ are given with $m$ significant bits, we provide for thefirst time an algorithm that finds all the roots of $f$ with a relativecondition number lower than $2^m$, using a number of bit operationsquasi-linear in the bit-size of the floating-point representation of $f$.Notably, our new approach handles efficiently polynomials with coefficientsranging from $2^{-d}$ to $2^d$, both in theory and in practice.

Fast evaluation and root finding for polynomials with floating-point coefficients