9 citations · 13 across the 8 of their papers we have counts for
8 papers
Reinforcement Learning for Power-Flow Network Analysis
Alperen Ergur, Julia Lindberg, Vinny Miller
The power flow equations are non-linear multivariate equations that describe the relationship between power injections and bus voltages of electric power networks. Given a network…
Beyond Worst-Case Analysis for Symbolic Computation: Root Isolation Algorithms
Alperen A. Ergür, Josué Tonelli-Cueto, Elias Tsigaridas
We introduce beyond-worst-case analysis into symbolic computation. This is an extensive field which almost entirely relies on worst-case bit complexity, and we start from a basic p…
On the Number of Real Zeros of Random Sparse Polynomial Systems
Alperen A. Ergür, Máté L. Telek, Josué Tonelli-Cueto
Consider a random system of random real polynomials in variables, where each has a prescribed set of expon…
The Geometry of Rank Drop in a Class of Face-Splitting Matrix Products
Erin Connelly, Sameer Agarwal, Alperen Ergur +1
Given points , we characterize rank deficiency of the matrix with rows in…
Beyond Worst-Case Analysis for Root Isolation Algorithms
Alperen A. Ergür, Josué Tonelli-Cueto, Elias Tsigaridas
Isolating the real roots of univariate polynomials is a fundamental problem in symbolic computation and it is arguably one of the most important problems in computational mathemati…
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…
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 the Number of Real Zeros of Random Fewnomials
Peter Bürgisser, Alperen A. Ergür, Josué Tonelli-Cueto
Consider a system of random real polynomials in variables, where each has a prescribed set of terms described by a set $A\subseteq \mathbb{…