Related papers: Recursive Matrix Algorithms in Commutative Domain …

A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths…

The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint…

We study the Parallel Replica Dynamics in a general setting. We introduce a trajectory fragment framework that can be used to design and prove consistency of Parallel Replica algorithms for generic Markov processes. We use our framework to…

Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…

We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use…

Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…

The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for its lack of…

We provide a mathematically proven parallelization scheme for particle methods on distributed-memory computer systems. Particle methods are a versatile and widely used class of algorithms for computer simulations and numerical predictions…

The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…

If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods…

We present an algorithm for cluster dynamics to efficiently simulate large systems on MIMD parallel computers with large numbers of processors. The method divides physical space into rectangular cells which are assigned to processors and…

Hierarchical matrices provide a highly memory-efficient way of storing dense linear operators arising, for example, from boundary element methods, particularly when stored in the H^2 format. In such data-sparse representations, iterative…

We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are…

Sparse matrix multiplication is an important component of linear algebra computations. In this paper, an architecture based on Content Addressable Memory (CAM) and Resistive Content Addressable Memory (ReCAM) is proposed for accelerating…

Parametric linear programming is a central operation for polyhedral computations, as well as in certain control applications.Here we propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.This type…

Second order stationary models in time series analysis are based on the analysis of essential statistics whose computations follow a common pattern. In particular, with a map-reduce nomenclature, most of these operations can be modeled as…

The multiplication of a sparse matrix with a dense vector (SpMV) is a key component in many numerical schemes and its performance is known to be severely limited by main memory access. Several numerical schemes require the multiplication of…

Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…

We consider a parallel computational model that consists of $P$ processors, each with a fast local ephemeral memory of limited size, and sharing a large persistent memory. The model allows for each processor to fault with bounded…

A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…