Zobrazeno 1 - 10
of 55
pro vyhledávání: '"Ergür, Alperen A."'
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 sequence that minimises the sum of dynamic time warping distances (DTW)
Externí odkaz:
http://arxiv.org/abs/2401.05841
Consider a random system $\mathfrak{f}_1(x)=0,\ldots,\mathfrak{f}_n(x)=0$ of $n$ random real polynomials in $n$ variables, where each $\mathfrak{f}_k$ has a prescribed set of exponent vectors in a set $A_k\subseteq \mathbb{Z}^n$ of size $t_k$. Assumi
Externí odkaz:
http://arxiv.org/abs/2306.06784
We investigate the effect of an $\varepsilon$-room of perturbation tolerance on symmetric tensor decomposition. To be more precise, suppose a real symmetric $d$-tensor $f$, a norm $||.||$ on the space of symmetric $d$-tensors, and $\varepsilon >0$ ar
Externí odkaz:
http://arxiv.org/abs/2207.12529
Publikováno v:
ACM Communications in Computer Algebra (2023) Vol. 57, No. 4
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 exponential complexity upper bound. Earlier computational results for
Externí odkaz:
http://arxiv.org/abs/2202.11582
Publikováno v:
Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation (ISSAC 22). Association for Computing Machinery, New York, NY, USA, 139-148 (2022)
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 mathematics. The problem has a long history decorated with numerous ingenious a
Externí odkaz:
http://arxiv.org/abs/2202.06428
Publikováno v:
Forum of Mathematics, Sigma (2022), Vol. 10:e103 1-49
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 complexity. In numerical polynomial algebra, a single norm (attributed to W
Externí odkaz:
http://arxiv.org/abs/2102.11727
Publikováno v:
Discrete & Computational Geometry, 68, pages 664-708 (2022)
We introduce tools from numerical analysis and high dimensional probability for precision control and complexity analysis of subdivision-based algorithms in computational geometry. We combine these tools with the continuous amortization framework fro
Externí odkaz:
http://arxiv.org/abs/2004.06879
Autor:
Ergür, Alperen A., de Wolff, Timo
Publikováno v:
Arnold Mathematical Journal, 2022
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 targeted for polynomial systems with coefficients satisfying certain
Externí odkaz:
http://arxiv.org/abs/1910.01957
Publikováno v:
SIAM Journal of Discrete Mathematics, Vol 36, Issue 2, 2022
Motivated by applications in combinatorial geometry, we consider the following question: Let $\lambda=(\lambda_1,\lambda_2,\ldots,\lambda_m)$ be an $m$-partition of a positive integer $n$, $S_i \subseteq \mathbb{C}^{\lambda_i}$ be finite sets, and le
Externí odkaz:
http://arxiv.org/abs/1910.01095
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 rate of low-density parity check codes. This formula vindicates a conje
Externí odkaz:
http://arxiv.org/abs/1906.05757