Related papers: HYLU: Hybrid Parallel Sparse LU Factorization

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;…

In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…

Positive linear programs (LPs) model many graph and operations research problems. One can solve for a $(1+\epsilon)$-approximation for positive LPs, for any selected $\epsilon$, in polylogarithmic depth and near-linear work via variations…

Sparse linear system solvers are computationally expensive kernels that lie at the heart of numerous applications. This paper proposes a flexible preconditioning framework to substantially reduce the time and energy requirements of this…

Matrix factorizations are among the most important building blocks of scientific computing. State-of-the-art libraries, however, are not communication-optimal, underutilizing current parallel architectures. We present novel algorithms for…

Krylov subspace methods are linear solvers based on matrix-vector multiplications and vector operations. While easily parallelizable, they are sensitive to rounding errors and may experience convergence issues. ILU(0), an incomplete LU…

We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…

This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions. This factorization takes the form of an approximate generalized LU…

This paper introduces cuHALLaR, a GPU-accelerated implementation of the HALLaR method proposed in Monteiro et al. 2024 for solving large-scale semidefinite programming (SDP) problems. We demonstrate how our Julia-based implementation…

The attention layer, a core component of Transformer-based LLMs, brings out inefficiencies in current GPU systems due to its low operational intensity and the substantial memory requirements of KV caches. We propose a High-bandwidth…

Hybrid parallelism underpins large-scale LLM training across tens of thousands of GPUs. At such scale, hardware failures on individual devices lead to performance skew across devices, diminishing overall training efficiency. Existing…

The increasing complexity in today's systems and the limited market times demand new development tools for FPGA. Currently, in addition to traditional hardware description languages (HDLs), there are high-level synthesis (HLS) tools that…

A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation…

The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…

Inspired by the developments in quantum computing, building domain-specific classical hardware to solve computationally hard problems has received increasing attention. Here, by introducing systematic sparsification techniques, we…

Matrix factorization (MF) is employed by many popular algorithms, e.g., collaborative filtering. The emerging GPU technology, with massively multicore and high intra-chip memory bandwidth but limited memory capacity, presents an opportunity…

The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on…

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…

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…

Recommendation systems, social network analysis, medical imaging, and data mining often involve processing sparse high-dimensional data. Such high-dimensional data are naturally represented as tensors, and they cannot be efficiently…