79 citations · 407 across the 53 of their papers we have counts for
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Certifying solutions to square systems of polynomial-exponential equations
Jonathan D. Hauenstein, Viktor Levandovskyy
Smale's alpha-theory certifies that Newton iterations will converge quadratically to a solution of a square system of analytic functions based on the Newton residual and all higher…
Algebraic boundaries of Hilbert's SOS cones
Grigoriy Blekherman, Jonathan Hauenstein, John Christian Ottem +2
We study the geometry underlying the difference between non-negative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and qu…
Numerically computing real points on algebraic sets
Jonathan D. Hauenstein
Given a polynomial system f, a fundamental question is to determine if f has real roots. Many algorithms involving the use of infinitesimal deformations have been proposed to answe…