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Using lower binomials to approximate roots of trinomials

MSRI-UP 2017: Solving Systems of Polynomial Equations June 24, 2017 - August 06, 2017

August 04, 2017 (01:00 PM PDT - 01:35 PM PDT)
Speaker(s): Harold Jimenez Polo (University of California, Berkeley), Esteban Madrigal (Harvard University), Carlos Osco Huaricapcha (San Francisco State University)
Location: MSRI: Baker Board Room
Video

Polo, Madrigal, Huaricapcha

Abstract

Given a univariate trinomial f in R[x], we analyze the Archimedean Newton polytope of f and the corresponding lower binomials. The roots of these lower binomials conjecturally provide high quality approximations of the roots of f. We implement Smale's alpha-criterion to analyze whether our approximations converge quickly under Newton iteration. We know that under certain conditions every root of a lower binomial is an approximate root of a trinomial. We expect to determine when at least one root of a lower binomial is an approximate root. Moreover, for roots that are not approximate, we examine when Newton's method yields approximate roots.

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Polo, Madrigal, Huaricapcha

H.264 Video Talk_4.mp4 1.11 GB video/mp4 rtsp://videos.msri.org/data/000/029/318/original/Talk_4.mp4 Download
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