Related papers: Computing Clipped Products
Model reduction, which aims to learn a simpler model of the original mixed integer linear programming (MILP), can solve large-scale MILP problems much faster. Most existing model reduction methods are based on variable reduction, which…
In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…
In this paper, we propose and study a fast multilevel dimension iteration (MDI) algorithm for computing arbitrary $d$-dimensional integrals based on tensor product approximations. It reduces the computational complexity (in terms of the CPU…
The rapid growth of demanding applications in domains applying multimedia processing and machine learning has marked a new era for edge and cloud computing. These applications involve massive data and compute-intensive tasks, and thus,…
Min-plus product of two $n\times n$ matrices is a fundamental problem in algorithm research. It is known to be equivalent to APSP, and in general it has no truly subcubic algorithms. In this paper, we focus on the min-plus product on a…
In this paper we study the Product Partition Problem (PPP), i.e. we are given a set of $n$ natural numbers represented on $m$ bits each and we are asked if a subset exists such that the product of the numbers in the subset equals the…
The notion of a generalized product, refining that of a (symmetric and smooth) simplicial space is introduced and shown to imply the existence of an algebra of pseudodifferential operators. This encompasses many constructions of such…
This article presents a vertical multiplication formula for calculating the multiplication of any two multi-digit integers, which may be not only used to design the multiplier but also to the mental multiplication. Our algorithm is a…
Prior to the recent development of symplectic integrators, the time-stepping operator $\e^{h(A+B)}$ was routinely decomposed into a sum of products of $\e^{h A}$ and $\e^{hB}$ in the study of hyperbolic partial differential equations. In…
We present algorithms for real and complex dot product and matrix multiplication in arbitrary-precision floating-point and ball arithmetic. A low-overhead dot product is implemented on the level of GMP limb arrays; it is about twice as fast…
A multiplier, as a key component in many different applications, is a time-consuming, energy-intensive computation block. Approximate computing is a practical design paradigm that attempts to improve hardware efficacy while keeping…
Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search…
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…
A product system E over a semigroup P is a family of Hilbert spaces {E_s:s\in P} together with multiplications E_s \times E_t\to E_{st}. We view E as a unitary- valued cocycle on P, and consider twisted crossed products A \times_{\beta,E} P…
We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We show how to construct polynomial schemes for the outer…
The main goal of this paper is to present new bounds for certain inner products in Hilbert spaces, with applications to the numerical radius and the operator norm. The obtained results significantly improve earlier results in this…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable…
We discuss a numerical package, named ORTHOCUB, for the computation of linear functionals of both integral and differential type on multivariate polynomial spaces. The weighted sums corresponding to such integral and differential cubatures…
Given a zero-dimensional ideal I in a polynomial ring, many computations start by finding univariate polynomials in I. Searching for a univariate polynomial in I is a particular case of considering the minimal polynomial of an element in…