<div dir="ltr">Merhabalar,<div><br></div><div>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. </div><div><br></div><div><div style="border-left:none;padding:0px;display:flex;font-family:"Google Sans",Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:medium"><div style="margin:0px;padding:0px 0px 20px;width:1092px"><div><div id="m_663059879022920988m_2444796939501045181gmail-:1kw" style="direction:ltr;margin:8px 0px 0px;padding:0px;font-size:0.875rem"><div id="m_663059879022920988m_2444796939501045181gmail-:13l" style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:small;line-height:1.5;font-family:Arial,Helvetica,sans-serif;overflow:hidden"><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div class="gmail_default"><div dir="ltr"><div dir="ltr"><div class="gmail_default">-----------------------------------------------------------------------------------<br><br><b>Başlık: </b> Polynomial Real Root Certification using Hermite Matrices over Q<br><br><b>Özet:</b> 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).<br>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.<br>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.<br>----------------------------------------------------------------------------------------<br><br><br>İyi Günler dilerim.<font color="#888888"><font color="#888888"><font color="#888888"><br>Temha<br></font></font></font></div></div></div></div></div></div></div></div></div><div class="gmail-yj6qo"></div><div class="gmail-adL"></div><div class="gmail-adL"></div><div class="gmail-adL"></div></div></div><div class="gmail-adL" style="border-bottom-left-radius:1px;border-bottom-right-radius:1px;padding:0px;width:auto;background:rgb(242,242,242);margin:0px"></div></div></div><div class="gmail-adL" style="clear:both"></div></div><div class="gmail-adL" style="font-size:0.875rem;padding:0px;width:auto;border-bottom-left-radius:0px;border-bottom-right-radius:0px;border-top:none;margin:0px;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial;font-family:"Google Sans",Roboto,RobotoDraft,Helvetica,Arial,sans-serif"><div style="border-top:0px;padding:0px"><div style="clear:both;margin:0px;padding:16px 0px;border-top:none"><br></div></div></div></div></div>
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