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Direct factorization methods for the solution of large, sparse linear systems that arise from PDE discretizations are robust, but typically show poor time and memory scalability for large systems. In this paper, we describe an efficient…
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…
We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…
FPGA architectures have recently been enhanced to meet the substantial computational demands of modern deep neural networks (DNNs). To this end, both FPGA vendors and academic researchers have proposed in-fabric blocks that perform…
In this paper, we address a long-standing challenge: how to achieve both efficiency and scalability in solving semidefinite programming problems. We propose breakthrough acceleration techniques for a wide range of low-rank…
Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental operation in graph computing and analytics. However, the irregularity of real-world graphs poses significant challenges to achieving efficient SpMM operation for graph data on…
Leveraging spatial sparsity has become a popular approach to accelerate 3D computer graphics applications. Spatially sparse data structures and efficient sparse kernels (such as parallel stencil operations on active voxels), are key to…
Architectural simulation has become the critical bottleneck limiting design space exploration for high-performance computing systems. Modern GPUs and AI accelerators -- with hundreds to thousands of tightly-coupled components -- demand…
We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use…
Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental computation in graph analytics, scientific simulation, and sparse deep learning workloads. However, the extreme irregularity of real-world sparse matrices prevents existing…
Systems of linear equations arise at the heart of many scientific and engineering applications. Many of these linear systems are sparse; i.e., most of the elements in the coefficient matrix are zero. Direct methods based on matrix…
We present Graphite, a GPU-accelerated nonlinear least squares graph optimization framework. It provides a CUDA C++ interface to enable the sharing of code between a real-time application, such as a SLAM system, and its optimization tasks.…
3D Gaussian Splatting (3DGS) has become a crucial rendering technique for many real-time applications. However, the limited hardware resources on today's mobile platforms hinder these applications, as they struggle to achieve real-time…
Sparse matrix-matrix multiplication (SpGEMM) is a critical kernel widely employed in machine learning and graph algorithms. However, real-world matrices' high sparsity makes SpGEMM memory-intensive. In-situ computing offers the potential to…
This paper explores the performance optimization of out-of-core (OOC) Cholesky factorization on shared-memory systems equipped with multiple GPUs. We employ fine-grained computational tasks to expose concurrency while creating opportunities…
B-spline modeling is fundamental to CAD systems, and its evaluation and manipulation algorithms currently in use were developed decades ago, specifically for CPU architectures. While remaining effective for many applications, these…
This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…
Matrix factorization (MF) is a widely used collaborative filtering (CF) algorithm for recommendation systems (RSs), due to its high prediction accuracy, great flexibility and high efficiency in big data processing. However, with the…
We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…
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…