Leonid Gurvits

Let $p(x_1,...,x_n) = p(X) , X \in R^{n}$ be a homogeneous polynomial of degree $n$ in $n$ real variables ,

$e = (1,1,..,1) \in R^n$ be a vector of all ones . Such polynomial $p$ is

called $e$-hyperbolic if for all real vectors $X \in R^{n}$ the univariate polynomial

equation ...
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Leonid Gurvits

We study in this paper randomized algorithms to approximate the mixed volume of well-presented convex compact sets.

Our main result is a poly-time algorithm which approximates $V(K_1,...,K_n)$ with multiplicative error $e^n$ and

with better rates if the affine dimensions of most of the sets $K_i$ are small.\\

Our approach is ...
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