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20142026
most citedProbabilistic Condition Number Estimates For Real Polynomial Systems I: A Broader Family Of Distributions

11 citations · 39 across the 14 of their papers we have counts for

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math.OC2016★ 2 cited

Approximating Nonnegative Polynomials via Spectral Sparsification

Alperen A. Ergür

We study polyhedral approximations to the cone of nonnegative polynomials. We show that any constant ratio polyhedral approximation to the cone of nonnegative degree forms in…

math.PR2016★ 11 cited

Probabilistic Condition Number Estimates For Real Polynomial Systems I: A Broader Family Of Distributions

Alperen A. Ergür, J. Maurice Rojas, Grigoris Paouris

We consider the sensitivity of real roots of polynomial systems with respect to perturbations of the coefficients. In particular - for a version of the condition number defined by…

math.AG2016★ 3 cited

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.