[Turkmath:5833] İ.Ü. Matematik Bölüm Semineri

[TEMHA ERKOÇ YILMAZTÜRK]

Merhabalar,

16.11.2022  tarihinde  saat 14.00 te   Karadeniz Teknik Üniversitesinden
Dr. Tülay Ayyıldız Akoğlu başlık ve özeti aşağıda verilen bir konuşma
yapacaktır. Seminer İ.Ü. Matematik Bölümü Cahit Arf Dershanesinde
yapılacaktır.

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*Başlık: * Polynomial Real Root Certification using Hermite Matrices over Q

*Özet:* 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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İyi Günler dilerim.
Temha

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