相关论文: Hyper-Systolic Matrix Multiplication

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we…

Systolic arrays have proven to be highly efficient for parallelized matrix-matrix multiplication (MMM), utilizing synchronized, heartbeat-like data flows across an array of processing elements. While optical structures such as waveguide…

Classic cache-oblivious parallel matrix multiplication algorithms achieve optimality either in time or space, but not both, which promotes lots of research on the best possible balance or tradeoff of such algorithms. We study modern…

The vision of super computer at every desk can be realized by powerful and highly parallel CPUs or GPUs or APUs. Graphics processors once specialized for the graphics applications only, are now used for the highly computational intensive…

We show that a particular class of parallel algorithm for linear functions can be straightforwardly generalized to a parallel algorithm of their tensor product. The central idea is to take a model of parallel algorithms -- Bulk Synchronous…

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…

This paper presents an efficient technique for matrix-vector and vector-transpose-matrix multiplication in distributed-memory parallel computing environments, where the matrices are unstructured, sparse, and have a substantially larger…

A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast…

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…

This article describes algorithms for the hybrid parallelization and SIMD vectorization of molecular dynamics simulations with short-range forces. The parallelization method combines domain decomposition with a thread-based parallelization…

We present a parallel FFT algorithm for SIMD systems following the `Transpose Algorithm' approach. The method is based on the assignment of the data field onto a 1-dimensional ring of systolic cells. The systolic array can be universally…

The growing interest for high dimensional and functional data analysis led in the last decade to an important research developing a consequent amount of techniques. Parallelized algorithms, which consist in distributing and treat the data…

Matrix multiplication consumes a large fraction of the time taken in many machine-learning algorithms. Thus, accelerator chips that perform matrix multiplication faster than conventional processors or even GPU's are of increasing interest.…

Generalized sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. Here we show that SpGEMM also yields efficient…

We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of this…

We present a multiscale integrator for Hamiltonian systems with slowly varying quadratic stiff potentials that uses coarse timesteps (analogous to what the impulse method uses for constant quadratic stiff potentials). This method is based…

While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…

The ability to express a program as a hierarchical composition of parts is an essential tool in managing the complexity of software and a key abstraction this provides is to separate the representation of data from the computation. Many…

In this paper we introduce a generic model for multiplicative algorithms which is suitable for the MapReduce parallel programming paradigm. We implement three typical machine learning algorithms to demonstrate how similarity comparison,…

Processor cores are becoming less expensive and thus more accessible. To utilize increasing number of available computing elements, good parallel algorithms are necessary. In light of these changes in contemporary computing, multipath…