11 citations · 39 across the 14 of their papers we have counts for
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A Polyhedral Homotopy Algorithm For Real Zeros
Alperen A. Ergür, Timo de Wolff
We design a homotopy continuation algorithm, that is based on numerically tracking Viro's patchworking method, for finding real zeros of sparse polynomial systems. The algorithm is…
Smoothed Analysis for the Condition Number of Structured Real Polynomial Systems
Alperen A. Ergür, Grigoris Paouris, J. Maurice Rojas
We consider the sensitivity of real zeros of structured polynomial systems to perturbations of their coefficients. In particular, we provide explicit estimates for condition number…
Multihomogenous Nonnegative Polynomials and Sums of Squares
Alperen Ergur
We refine and extend quantitative bounds, on the fraction of nonnegative polynomials that are sums of squares, to the multihomogenous case.
Tropical Varieties for Exponential Sums
Alperen Ergür, Grigoris Paouris, J. Maurice Rojas
We study the complexity of approximating complex zero sets of certain -variate exponential sums. We show that the real part, , of such a zero set can be approximated by the $…