Related papers: A divide-and-conquer algorithm for computing Gr\"o…
Bayesian computational algorithms tend to scale poorly as data size increases. This has motivated divide-and-conquer-based approaches for scalable inference. These divide the data into subsets, perform inference for each subset in parallel,…
Based on functional analysis, we propose an algorithm for finite-norm solutions of higher-order linear Fuchsian-type ordinary differential equations (ODEs) P(x,d/dx)f(x)=0 with P(x,d/dx):=[\sum_m p_m (x) (d/dx)^m] by using only the four…
Computations over the rational numbers often encounter the problem of intermediate coefficient growth. A solution to this is provided by modular methods, which apply the algorithm under consideration modulo a number of primes and then lift…
For a finite $\mathbb{Z}$-algebra $R$, i.e., for a $\mathbb{Z}$-algebra which is a finitely generated $\mathbb{Z}$-module, we assume that $R$ is explicitly given by a system of $\mathbb{Z}$-module generators $G$, its relation module ${\rm…
Gradient Boosting Machine (GBM) introduced by Friedman is a powerful supervised learning algorithm that is very widely used in practice---it routinely features as a leading algorithm in machine learning competitions such as Kaggle and the…
We present an engineered version of the divide-and-conquer algorithm for finding the closest pair of points, within a given set of points in the XY-plane. For this version of the algorithm we show that only two pairwise comparisons are…
In this work we present a way to construct the so-called root diagram for one-point AG codes $C$ arising from certain types of curves $\mathcal{X}$ over $\mathbb{F}_q$ with plane model $f(y)=g(x)$. Using this root diagram we can get an…
We study the complexity of Gr\"obner bases computation, in particular in the generic situation where the variables are in simultaneous Noether position with respect to the system. We give a bound on the number of polynomials of degree $d$…
Algorithmic computation in polynomial rings is a classical topic in mathematics. However, little attention has been given to the case of rings with an infinite number of variables until recently when theoretical efforts have made possible…
We study efficient distributed algorithms for the fundamental problem of principal component analysis and leading eigenvector computation on the sphere, when the data are randomly distributed among a set of computational nodes. We propose a…
We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (\emph{Tiling for Binary Matrix Completion}), gives interpretable output in the…
Two square matrices of (arbitrary) order N are introduced. They are defined in terms of N arbitrary numbers z_{n}, and of an arbitrary additional parameter (a respectively q), and provide finite-dimensional representations of the two…
Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example…
This article provides a comprehensive exploration of submodular maximization problems, focusing on those subject to uniform and partition matroids. Crucial for a wide array of applications in fields ranging from computer science to systems…
We develop the theory of Gr\"obner bases for ideals in a polynomial ring with countably infinite variables over a field. As an application we reconstruct some of the one-one correspondences among various sets of partitions by using division…
For the ideal $I = \langle y_1 + \dots + y_n, y^2_1, \dots , y^2_n \rangle$ in $R = {\mathbb F}[y_1, \dots , y_n]$ with char($\mathbb F$) = 0, we show that the reduced Gr\"obner basis with lex-order consists of polynomials $g_\alpha$ that…
In this thesis, a new approach for constructing subdivision algorithms for generalized quadratic and cubic B-spline subdivision for subdivision surfaces and volumes is presented. First, a catalog of quality criteria for these subdivision…
We present a new algorithm for computing a $\mu$-basis of the syzygy module of $n$ polynomials in one variable over an arbitrary field $\mathbb{K}$. The algorithm is conceptually different from the previously-developed algorithms by Cox,…
A classical problem in Distance Geometry, with multiple practical applications (in molecular structure determination, sensor network localization etc.) is to find the possible placements of the vertices of a graph with given edge lengths.…
We develop a method for approximating the Gr\"obner basis of the ideal of polynomials which vanish at a finite set of points, when the coordinates of the points are known with only limited precision. The method consists of a preprocessing…