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DESCRIPTION: Solving systems of polynomial equations is one of the oldest a
nd most important problems in computational mathematics and has many applic
ations in several domains of science and engineering. It is an intrinsicall
y hard problem with complexity at least single exponential in the number of
variables. However\, in most of the cases\, the polynomial systems coming
from applications have some kind of structure. For example\, several proble
ms in computer-aided design\, robotics\, computer vision\, molecular biolog
y and kinematics involve polynomial systems that are sparse that is\, only
a few monomials have non-zero coefficients. We focus on exploiting the sp
arsity of the Newton polytopes of the polynomials to solve the systems fast
er than the worst case estimates. In this talk\, I will present a Gröbner b
asis approach to solve sparse 0-dimensional systems whose input polynomials
have different Newton polytopes. Under regularity assumptions\, we can hav
e an explicit combinatorial bound for the complexity of the algorithm. Th
is is joint work with Jean-Charles Faugère and Elias Tsigaridas.
DTSTAMP:20190114T154500
DTSTART:20190211T160000
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9
\n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Matías Bender (Sorbonne Université Paris): Solving sparse polynomia
l systems using Gröbner basis
UID:95690447@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20190211-C-Bender.html
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