11 citations · 39 across the 14 of their papers we have counts for
15 papers
Approximating CDTW Distance of Piecewise Algebraic Curves
Alperen A. Ergür, Shamik Khowala
Curves as input data naturally arise in a variety of fields including finance, seismology, medicine, spatio-temporal data mining, malicious activity detection, and more. A common w…
Learning Fast Monomial Orders for Gröbner Basis Computations
R. Caleb Bunch, Alperen A. Ergür, Melika Golestani +3
The efficiency of Gröbner basis computation, the standard engine for solving systems of polynomial equations, depends on the choice of monomial ordering. Despite a near-continuum o…
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…
On the number of iterations of the DBA algorithm
Frederik Brüning, Anne Driemel, Alperen Ergür +1
The DTW Barycenter Averaging (DBA) algorithm is a widely used algorithm for estimating the mean of a given set of point sequences. In this context, the mean is defined as a point s…
Approximate Real Symmetric Tensor Rank
Alperen A. Ergür, Jesus Rebollo Bueno, Petros Valettas
We investigate the effect of an -room of perturbation tolerance on symmetric tensor decomposition. To be more precise, suppose a real symmetric -tensor , a norm…
On the complexity of Chow and Hurwitz forms
Mahmut Levent Doğan, Alperen Ali Ergür, Elias Tsigaridas
We consider the bit complexity of computing Chow forms and their generalization to multiprojective spaces. We develop a deterministic algorithm using resultants and obtain a single…
A Polyhedral Homotopy Algorithm For Real Zeros
Alperen A. Ergür, Timo de Wolff
We design a homotopy continuation algorithm, that is based on numerically tracking Viro's patchworking method, for finding real zeros of sparse polynomial systems. The algorithm is…
The Multivariate Schwartz-Zippel Lemma
M. Levent Doğan, Alperen A. Ergür, Jake D. Mundo +1
Motivated by applications in combinatorial geometry, we consider the following question: Let be an -partition of a positive integer , $S_i \subseteq…
The rank of sparse random matrices
Amin Coja-Oghlan, Alperen A. Ergür, Pu Gao +2
We determine the rank of a random matrix over an arbitrary field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the r…
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…
Smoothed Analysis for the Condition Number of Structured Real Polynomial Systems
Alperen A. Ergür, Grigoris Paouris, J. Maurice Rojas
We consider the sensitivity of real zeros of structured polynomial systems to perturbations of their coefficients. In particular, we provide explicit estimates for condition number…
Approximating Nonnegative Polynomials via Spectral Sparsification
Alperen A. Ergür
We study polyhedral approximations to the cone of nonnegative polynomials. We show that any constant ratio polyhedral approximation to the cone of nonnegative degree forms in…
Probabilistic Condition Number Estimates For Real Polynomial Systems I: A Broader Family Of Distributions
Alperen A. Ergür, J. Maurice Rojas, Grigoris Paouris
We consider the sensitivity of real roots of polynomial systems with respect to perturbations of the coefficients. In particular - for a version of the condition number defined by…
Multihomogenous Nonnegative Polynomials and Sums of Squares
Alperen Ergur
We refine and extend quantitative bounds, on the fraction of nonnegative polynomials that are sums of squares, to the multihomogenous case.
Tropical Varieties for Exponential Sums
Alperen Ergür, Grigoris Paouris, J. Maurice Rojas
We study the complexity of approximating complex zero sets of certain -variate exponential sums. We show that the real part, , of such a zero set can be approximated by the $…