14 citations · 53 across the 17 of their papers we have counts for
6 papers · 1 filter
On the Error of Random Sampling: Uniformly Distributed Random Points on Parametric Curves
Apostolos Chalkis, Christina Katsamaki, Josué Tonelli-Cueto
Given a parametric polynomial curve , how can we sample a random point in such a way that it is distributed unifor…
Condition Numbers for the Cube. I: Univariate Polynomials and Hypersurfaces
Josué Tonelli-Cueto, Elias Tsigaridas
The condition-based complexity analysis framework is one of the gems of modern numerical algebraic geometry and theoretical computer science. Among the challenges that it poses is…
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.…
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…
Computing the Homology of Semialgebraic Sets I: Lax Formulas
Peter Bürgisser, Felipe Cucker, Josué Tonelli-Cueto
We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of closed semialgebraic sets given by Boolean formulas without negations ov…