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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…

In this paper, we aim to introduce a new perspective when comparing highly parallelized algorithms on GPU: the energy consumption of the GPU. We give an analysis of the performance of linear algebra operations, including addition of…

Recently, graphics processors (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage…

We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…

We present parallel algorithms for constructing and traversing sparse octrees on graphics processing units (GPUs). The algorithms are based on parallel-scan and sort methods. To test the performance and feasibility, we implemented them in…

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…

Despite numerous efforts for optimizing the performance of Sparse Matrix and Vector Multiplication (SpMV) on modern hardware architectures, few works are done to its sparse counterpart, Sparse Matrix and Sparse Vector Multiplication…

This paper is focused on the improvement the efficiency of the sparse convolutional neural networks (CNNs) layers on graphic processing units (GPU). The Nvidia deep neural network (cuDnn) library provides the most effective implementation…

We propose an algorithm for rotational sparse coding along with an efficient implementation using steerability. Sparse coding (also called dictionary learning) is an important technique in image processing, useful in inverse problems,…

Recent works demonstrate the advantages of hardware rasterization for 3D Gaussian Splatting (3DGS) in forward-pass rendering through fast GPU-optimized graphics and fixed memory footprint. However, extending these benefits to backward-pass…

An alias table is a data structure that allows for efficiently drawing weighted random samples in constant time and can be constructed in linear time. The PSA algorithm by H\"ubschle-Schneider and Sanders is able to construct alias tables…

Large Transformer models yield impressive results on many tasks, but are expensive to train, or even fine-tune, and so slow at decoding that their use and study becomes out of reach. We address this problem by leveraging sparsity. We study…

We consider the problem of sparse signal recovery from a small number of random projections (measurements). This is a well known NP-hard to solve combinatorial optimization problem. A frequently used approach is based on greedy iterative…

As the size of Deep Neural Networks (DNNs) increases dramatically to achieve high accuracy, the DNNs require a large amount of computations and memory footprint. Pruning, which produces a sparse neural network, is one of the solutions to…

Sparse matrix-matrix multiplication (SpGEMM) is a critical operation in numerous fields, including scientific computing, graph analytics, and deep learning. These applications exploit the sparsity of matrices to reduce storage and…

Ordering vertices of a graph is key to minimize fill-in and data structure size in sparse direct solvers, maximize locality in iterative solvers, and improve performance in graph algorithms. Except for naturally parallelizable ordering…

The sparse matrix-vector (SpMV) multiplication is an important computational kernel, but it is notoriously difficult to execute efficiently. This paper investigates algorithm performance for unstructured sparse matrices, which are more…

General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method (AMG), breadth first search and shortest path problem. Compared to other sparse BLAS routines,…

Sparse matrix-vector multiplication is often employed in many data-analytic workloads in which low latency and high throughput are more valuable than exact numerical convergence. FPGAs provide quick execution times while offering precise…

Generalized inverses play a fundamental role in numerical linear algebra, particularly when matrices are rectangular, singular, or rank deficient. Even when the input matrix is sparse, generalized inverses such as the M-P pseudoinverse are…