36 citations · 196 across the 30 of their papers we have counts for
32 papers
Functional norms, condition numbers and numerical algorithms in algebraic geometry
Felipe Cucker, Alperen A. Ergür, Josué Tonelli-Cueto
In numerical linear algebra, a well-established practice is to choose a norm that exploits the structure of the problem at hand in order to optimize accuracy or computational compl…
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…
On the Complexity of the Plantinga-Vegter Algorithm
Felipe Cucker, Alperen A. Ergür, Josué Tonelli-Cueto
We introduce tools from numerical analysis and high dimensional probability for precision control and complexity analysis of subdivision-based algorithms in computational geometry.…
On local analysis
Felipe Cucker, Teresa Krick
We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion…
Computing the Homology of Semialgebraic Sets. II: General formulas
Peter Bürgisser, Felipe Cucker, Josué Tonelli-Cueto
We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of semialgebraic sets given by Boolean formulas. The algorithm wor…
Plantinga-Vegter algorithm takes average polynomial time
Felipe Cucker, Alperen A. Ergür, Josue Tonelli-Cueto
We exhibit a condition-based analysis of the adaptive subdivision algorithm due to Plantinga and Vegter. The first complexity analysis of the PV Algorithm is due to Burr, Gao and T…