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math.NA2020
Rigid continuation paths II. Structured polynomial systems
Peter Bürgisser, Felipe Cucker, Pierre Lairez
This work studies the average complexity of solving structured polynomial systems that are characterized by a low evaluation cost, as opposed to the dense random model previously u…
math.NA2017★ 2 cited
Rigid continuation paths I. Quasilinear average complexity for solving polynomial systems
Pierre Lairez
How many operations do we need on the average to compute an approximate root of a random Gaussian polynomial system? Beyond Smale's 17th problem that asked whether a polynomial bou…
math.NA2015★ 25 cited
A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time
Pierre Lairez
We describe a deterministic algorithm that computes an approximate root of n complex polynomial equations in n unknowns in average polynomial time with respect to the size of the i…