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Title:
Using lower binomials to approximate roots of trinomials

Speaker:
Harold Jimenez Polo

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.

Link:
https://www.msri.org/msri_ups/806/schedules/22878

Workshop:
MSRI- MSRI-UP 2017: Solving Systems of Polynomial Equations