[Turkmath:5824] Gebze Teknik Üniversitesi Matematik Bölümü Genel Seminerleri

[GTU Mathematics]

Sayin Liste Uyeleri,

Gebze Teknik Üniversitesi (GTU) Matematik Bölümü Genel Seminerleri
kapsamında, 11 Kasım Cuma günü saat 14:00'te Dr. Tülay Ayyıldız Akoğlu
(Karadeniz
Teknik Üniversitesi ve İstanbul Teknik Üniversitesi) bir seminer
verecektir. Seminerin detayları aşağıda olup tüm ilgilenenler davetlidir.

Saygılarımızla.

Dear all,

There will be a seminar in Gebze Technical University (GTU) on 11th of
November by Dr. Tülay Ayyıldız Akoğlu (Karadeniz Technical University and
İstanbul Technical University).

Time and place: At 14:00 in Department of Mathematics, Lecture Room 3

Title: Polynomial Real Root Certification using Hermite Matrices over Q
Abstract: Polynomial systems can be solved reliably using numerical
homotopy methods. These methods return numerical approximations to
solutions, and all the implementations validate the solutions
heuristically. Therefore, the output, the approximate solutions of
polynomial systems are not certified. Even though the approximate solutions
work well in practice, they cannot be used in critical applications,
especially in pure mathematics or when high precision is needed (eg.
Surgical Robot arm applications).
Let I be a zero dimensional and radical ideal generated by m polynomials
with exact rational coefficients. Assume that we are given approximations
for the common exact roots.
In this talk, we show how to construct and certify the rational entries of
Hermite matrices for I from the approximate roots. Furthermore, we
represent a method to certify the real roots of the given polynomial system
using the signature of Hermite matrices.
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