Using lower binomials to approximate roots of trinomials
MSRIUP 2017: Solving Systems of Polynomial Equations June 24, 2017  August 06, 2017
Location: SLMath: Baker Board Room
Polo, Madrigal, Huaricapcha
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 alphacriterion 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.
Polo, Madrigal, Huaricapcha
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