123 citations · 479 across the 28 of their papers we have counts for
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math.AG2011★ 6 cited
On the expected number of zeros of nonlinear equations
Gregorio Malajovich
This paper investigates the expected number of complex roots of nonlinear equations. Those equations are assumed to be analytic, and to belong to certain inner product spaces. Thos…
math.NA2011★ 33 cited
Adaptative Step Size Selection for Homotopy Methods to Solve Polynomial Equations
Jean-Pierre Dedieu, Gregorio Malajovich, Michael Shub
Given a C^1 path of systems of homogeneous polynomial equations f_t, t in [a,b] and an approximation x_a to a zero zeta_a of the initial system f_a, we show how to adaptively choos…