Related papers: $n$th Roots of $n$th Powers

Graphics Processing Units (GPUs) are high performance co-processors originally intended to improve the use and quality of computer graphics applications. Once, researchers and practitioners noticed the potential of using GPU for general…

Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without…

We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…

Graphics Processing Units (GPUs) are now powerful and flexible systems adapted and used for other purposes than graphics calculations (General Purpose computation on GPU -- GPGPU). We present here a prototype to be integrated into…

Optimal usage of the memory system is a key element of fast GPU algorithms. Unfortunately many common algorithms fail in this regard despite exhibiting great regularity in memory access patterns. In this paper we propose efficient kernels…

Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…

GPUs have significantly accelerated first-order methods for large-scale optimization, especially in continuous optimization. However, this success has not transferred cleanly to problems with discrete variables, combinatorial structure, and…

The development of large-scale, programmable photonic circuits capable of performing generic matrix-vector multiplication is essential for both classical and quantum information processing. However, this goal is hindered by high losses,…

A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…

In this paper we consider parallelization for applications whose objective can be expressed as maximizing a non-monotone submodular function under a cardinality constraint. Our main result is an algorithm whose approximation is arbitrarily…

We use recent results on algorithms for Markov decision problems to show that a canonical form for a generalized P-matrix can be computed, in some important cases, by a strongly polynomial algorithm.

General-purpose computing on graphics processing units (GPGPU) has recently gained considerable attention in various domains such as bioinformatics, databases and distributed computing. GPGPU is based on using the GPU as a co-processor…

Optimal power flow (OPF) is a critical optimization problem that allocates power to the generators in order to satisfy the demand at a minimum cost. Solving this problem exactly is computationally infeasible in the general case. In this…

We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…

Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering, and underlies the solution of time-homogeneous linear ordinary differential equations,…

Due to their highly parallel multi-cores architecture, GPUs are being increasingly used in a wide range of computationally intensive applications. Compared to CPUs, GPUs can achieve higher performances at accelerating the programs'…

The Unigram tokenization algorithm offers a probabilistic alternative to the greedy heuristics of Byte-Pair Encoding. Despite its theoretical elegance, its implementation in practice is complex, limiting its adoption to the SentencePiece…

Memoryless computation is a novel means of computing any function of a set of registers by updating one register at a time while using no memory. We aim to emulate how computations are performed on modern cores, since they typically involve…

We describe the use of Graphics Processing Units (GPUs) for speeding up the code NBODY6 which is widely used for direct $N$-body simulations. Over the years, the $N^2$ nature of the direct force calculation has proved a barrier for…

The study of biological systems witnessed a pervasive cross-fertilization between experimental investigation and computational methods. This gave rise to the development of new methodologies, able to tackle the complexity of biological…