相关论文: Hyper-Systolic Matrix Multiplication

Previous parallel sorting algorithms do not scale to the largest available machines, since they either have prohibitive communication volume or prohibitive critical path length. We describe algorithms that are a viable compromise and…

The Massive Parallel Computing (MPC) model gained popularity during the last decade and it is now seen as the standard model for processing large scale data. One significant shortcoming of the model is that it assumes to work on static…

We give an overview of the theoretical results for matrix block-recursive algorithms in commutative domains and present the results of experiments that we conducted with new parallel programs based on these algorithms on a supercomputer…

We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…

We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…

Parallel matrix multiplication is one of the most studied fundamental problems in distributed and high performance computing. We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes…

In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…

An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent…

We describe a new algorithm for Gaussian Elimination suitable for general (unsymmetric and possibly singular) sparse matrices, of any entry type, which has a natural parallel and distributed-memory formulation but degrades gracefully to…

Matrix Distributed Processing (MDP) is a C++ library for fast development of efficient parallel algorithms. It constitues the core of FermiQCD. MDP enables programmers to focus on algorithms, while parallelization is dealt with…

A parallel algorithm has perfect strong scaling if its running time on P processors is linear in 1/P, including all communication costs. Distributed-memory parallel algorithms for matrix multiplication with perfect strong scaling have only…

A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select…

Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…

We propose new sequential sorting operations by adapting techniques and methods used for designing parallel sorting algorithms. Although the norm is to parallelize a sequential algorithm to improve performance, we adapt a contrarian…

In science and engineering, intelligent processing of complex signals such as images, sound or language is often performed by a parameterized hierarchy of nonlinear processing layers, sometimes biologically inspired. Hierarchical systems…

Multilevel/multigrid methods is one of the most popular approaches for solving a large sparse linear system of equations, typically, arising from the discretization of partial differential equations. One critical step in the…

We present a recursive way to partition hypergraphs which creates and exploits hypergraph geometry and is suitable for many-core parallel architectures. Such partitionings are then used to bring sparse matrices in a recursive Bordered Block…

Scaling up the sparse matrix-vector multiplication kernel on modern Graphics Processing Units (GPU) has been at the heart of numerous studies in both academia and industry. In this article we present a novel non-parametric, self-tunable,…

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…

Traditional heterogeneous parallel algorithms, designed for heterogeneous clusters of workstations, are based on the assumption that the absolute speed of the processors does not depend on the size of the computational task. This assumption…