most recent 30 from http://mathoverflow.net 2013-05-20T12:24:19Z http://mathoverflow.net/feeds/question/91627 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/91627/computing-a-determinantal-representation-of-a-bivariate-polynomial alext87 2012-03-19T15:46:52Z 2012-10-24T08:52:41Z

<p>Let $p(x,y,z)$ be a homogeneous irreducible polynomial of degree $d$, with real coefficients. From Dickson in 1920 we know that there exists $A$, $B$ and $C$ such that </p> <p>$ det(Ax + By + Cz) = c p(x,y,z)$,</p> <p>where $c$ is some constant. </p> <p>Vinnokov in 1988 was able to describe all the non-equivalent determinantal representations as points on the Jacobian variety that are not on the exceptional sub variety. The theoretical work in this paper is relatively constructive, but is still a long way from a numerically stable constructive algorithm for $A$, $B$ and $C$. </p> <p>Given any polynomial $p(x,y,z)$, can one triple $(A, B,C)$ be constructed in a numerically stable way?</p> <p>Thanks in advance. </p>

http://mathoverflow.net/questions/91627/computing-a-determinantal-representation-of-a-bivariate-polynomial/110524#110524 Markus Schweighofer 2012-10-24T08:52:41Z 2012-10-24T08:52:41Z

<p>This is discussed in a recent work of Plaumann, Sturmfels and Vinzant:</p> <p><a href="http://arxiv.org/abs/1011.6057" rel="nofollow">http://arxiv.org/abs/1011.6057</a></p>