相关论文: GSoFa: Scalable Sparse Symbolic LU Factorization o…
We discuss an approach for solving sparse or dense banded linear systems ${\bf A} {\bf x} = {\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\bf A} \in {\mathbb{R}}^{N \times N}$ is possibly nonsymmetric and moderately large;…
Benefiting from the self-attention mechanism, Transformer models have attained impressive contextual comprehension capabilities for lengthy texts. The requirements of high-throughput inference arise as the large language models (LLMs)…
The practical scalability of many optimization algorithms for large extensive-form games is often limited by the games' huge payoff matrices. To ameliorate the issue, Zhang and Sandholm (2020) recently proposed a sparsification technique…
Scalable sparse LU factorization is critical for efficient numerical simulation of circuits and electrical power grids. In this work, we present a new scalable sparse direct solver called Basker. Basker introduces a new algorithm to…
Selected inversion is essential for applications such as Bayesian inference, electronic structure calculations, and inverse covariance estimation, where computing only specific elements of large sparse matrix inverses significantly reduces…
The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…
We describe a method for parallelizing the lexicographic enumeration algorithm for the factorization set of an element in a numerical semigroup via bounds. This enables the use of GPU and distributed computing methods. We provide a CUDA…
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,…
We study parallel algorithms for the minimisation and equivalence checking of Deterministic Finite Automata (DFAs). Regarding DFA minimisation, we implement four different massively parallel algorithms on Graphics Processing Units~(GPUs).…
Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…
Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which…
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…
Fill-ins are new nonzero elements in the summation of the upper and lower triangular factors generated during LU factorization. For large sparse matrices, they will increase the memory usage and computational time, and be reduced through…
High-throughput imaging workflows, such as Parallel Rapid Imaging with Spectroscopic Mapping (PRISM), generate data at rates that exceed conventional real-time processing capabilities. We present a scalable FPGA-based preprocessing pipeline…
We describe an efficient parallel implementation of the selected inversion algorithm for distributed memory computer systems, which we call \texttt{PSelInv}. The \texttt{PSelInv} method computes selected elements of a general sparse matrix…
The rapid growth of Large Language Models has driven demand for effective model compression techniques to reduce memory and computation costs. Low-rank pruning has gained attention for its GPU compatibility across all densities. However,…
Due to importance of reducing of time solution in numerical codes, we propose an algorithm for parallel LU decomposition solver for dense and sparse matrices on GPU. This algorithm is based on first bi-vectorizing a triangular matrices of…
This research investigates the implementation mechanism of block-wise ILU(k) preconditioner on GPU. The block-wise ILU(k) algorithm requires both the level k and the block size to be designed as variables. A decoupled ILU(k) algorithm…
A High-dimensional and sparse (HiDS) matrix is frequently encountered in a big data-related application like an e-commerce system or a social network services system. To perform highly accurate representation learning on it is of great…
Low-rank methods have shown success in accelerating simulations of a collisionless plasma described by the Vlasov equation, but still rely on computationally costly linear algebra every time step. We propose a data-driven factorization…