77 citations · 197 across the 43 of their papers we have counts for
51 papers
Resultant multiplicity via projective degrees and applications to tensor eigenvalues
Mahmut Levent Doğan, Elias Tsigaridas, Zafeirakis Zafeirakopoulos
Given a system of homogeneous forms in variables of the same degree, Macaulay's resultant vanishes precisely when the polynomials have a commo…
Exact Algebraic Computation of Learning Coefficients for Two-Dimensional Singular Models
Grégoire Sergeant-Perthuis, Elias Tsigaridas, Jules Tsukahara
Classical information criteria such as the Bayesian Information Criterion (BIC) rely on regularity assumptions that break down for singular models, leading to incorrect model selec…
Small Resultant Systems via Linear Combinations
M. Levent Doğan, Elias Tsigaridas, Zafeirakis Zafeirakopoulos
For a system of homogeneous polynomials of degree in variables, say , we consider the problem of constructing resultant systems. A resultant system is a f…
Optimal Preconditioning is a Geodesically Convex Optimization Problem
M. Levent Doğan, Alperen Ergür, Elias Tsigaridas
We introduce a unified framework for computing approximately-optimal preconditioners for solving linear and non-linear systems of equations. We demonstrate that the condition numbe…
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…
Bounds on the infimum of polynomials over a generic semi-algebraic set using asymptotic critical values
Boulos El Hilany, Elias Tsigaridas
We present precise bit and degree estimates for the optimal value of the polynomial optimization problem , where is a semi-al…