Related papers: Efficient Multiplication of Dense Matrices over GF…
In this paper, we present algorithms to solve matrix multiplication problems in the MPC model. In particular, we consider the problem under various processor/memory constraints in the MPC model and prove the following results. 1.…
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…
We present a method for parallel block-sparse matrix-matrix multiplication on distributed memory clusters. By using a quadtree matrix representation, data locality is exploited without prior information about the matrix sparsity pattern. A…
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…
We approach the problem of implementing mixed-datatype support within the general matrix multiplication (GEMM) operation of the BLIS framework, whereby each matrix operand A, B, and C may be stored as single- or double-precision real or…
Frequent Subgraph Mining (FSM) is the key task in many graph mining and machine learning applications. Numerous systems have been proposed for FSM in the past decade. Although these systems show good performance for small patterns (with no…
Solving and visualizing the potential roots of complex functions is essential in both theoretical and applied domains, yet often computationally intensive. We present a hardware-accelerated algorithm for complex function roots density graph…
Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time…
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…
We present efficient algorithms to build data structures and the lists needed for fast multipole methods. The algorithms are capable of being efficiently implemented on both serial, data parallel GPU and on distributed architectures. With…
Optical neural networks (ONN) based on micro-ring resonators (MRR) have emerged as a promising alternative to significantly accelerating the massive matrix-vector multiplication (MVM) operations in artificial intelligence (AI) applications.…
NVIDIA Tensor Core is a mixed-precision matrix-matrix multiplication and addition computing unit, where the theoretical peak performance is more than 300 TFlop/s on NVIDIA A100 GPU. NVIDIA provides WMMA API for using Tensor Cores in custom…
KBLAS is a new open source high performance library that provides optimized kernels for a subset of Level 2 BLAS functionalities on CUDA-enabled GPUs. Since performance of dense matrix-vector multiplication is hindered by the overhead of…
Augmenting the balanced residue number system moduli-set $\{m_1=2^n,m_2=2^n-1,m_3=2^n+1\}$, with the co-prime modulo $m_4=2^{2n}+1$, increases the dynamic range (DR) by around 70%. The Mersenne form of product $m_2 m_3 m_4=2^{4n}-1$, in the…
This paper presents a low-latency hardware accelerator for modular polynomial multiplication for lattice-based post-quantum cryptography and homomorphic encryption applications. The proposed novel modular polynomial multiplier exploits the…
Neural networks with a latency requirement on the order of microseconds, like the ones used at the CERN Large Hadron Collider, are typically deployed on FPGAs fully unrolled and pipelined. A bottleneck for the deployment of such neural…
We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…
This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel…
The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a…
Matrix multiplication (MatMul) is the computational backbone of modern machine learning, yet its classical complexity remains a bottleneck for large-scale data processing. We propose a hybrid quantum-classical algorithm for matrix…