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06/16/2022
Ultrametric Smale's α-theory
We present a version of Smale's α-theory for ultrametric fields, such as...
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03/14/2022
A p-adic Descartes solver: the Strassman solver
Solving polynomials is a fundamental computational problem in mathematic...
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03/05/2022
On the Error of Random Sampling: Uniformly Distributed Random Points on Parametric Curves
Given a parametric polynomial curve γ:[a,b]→ℝ^n, how can we sample a ran...
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02/13/2022
Beyond Worst-Case Analysis for Root Isolation Algorithms
Isolating the real roots of univariate polynomials is a fundamental prob...
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02/23/2021
Functional norms, condition numbers and numerical algorithms in algebraic geometry
In numerical linear algebra, a well-established practice is to choose a ...
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06/08/2020
Condition Numbers for the Cube. I: Univariate Polynomials and Hypersurfaces
The condition-based complexity analysis framework is one of the gems of ...
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04/15/2020
On the Complexity of the Plantinga-Vegter Algorithm
We introduce a general toolbox for precision control and complexity anal...
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03/26/2019
Computing the Homology of Semialgebraic Sets. II: General formulas
We describe and analyze an algorithm for computing the homology (Betti n...
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01/26/2019
Plantinga-Vegter algorithm takes average polynomial time
We exhibit a condition-based analysis of the adaptive subdivision algori...
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07/10/2018