Related papers: Level-based Blocking for Sparse Matrices: Sparse M…
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…
Graph neural networks (GNNs) are emerging as a powerful technique for modeling graph structures. Due to the sparsity of real-world graph data, GNN performance is limited by extensive sparse matrix multiplication (SpMM) operations involved…
In a large-scale and distributed matrix multiplication problem $C=A^{\intercal}B$, where $C\in\mathbb{R}^{r\times t}$, the coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may…
Designing efficient and scalable sparse linear algebra kernels on modern multi-GPU based HPC systems is a daunting task due to significant irregular memory references and workload imbalance across the GPUs. This is particularly the case for…
Recently, the sparse vector code (SVC) is emerging as a promising solution for short-packet transmission in massive machine type communication (mMTC) as well as ultra-reliable and low-latency communication (URLLC). In the SVC process, the…
Although the matrix multiplication plays a vital role in computational linear algebra, there are few efficient solutions for matrix multiplication of the near-sparse matrices. The Sparse Approximate Matrix Multiply (SpAMM) is one of the…
Important workloads, such as machine learning and graph analytics applications, heavily involve sparse linear algebra operations. These operations use sparse matrix compression as an effective means to avoid storing zeros and performing…
Recent work has demonstrated that using a carefully designed sensing matrix rather than a random one, can improve the performance of compressed sensing. In particular, a well-designed sensing matrix can reduce the coherence between the…
Large-scale machine learning (ML) models are increasingly being used in critical domains like education, lending, recruitment, healthcare, criminal justice, etc. However, the training, deployment, and utilization of these models demand…
We present a highly scalable algorithm for multiplying sparse multivariate polynomials represented in a distributed format. This algo- rithm targets not only the shared memory multicore computers, but also computers clusters or specialized…
The Sparse GEneral Matrix-Matrix multiplication (SpGEMM) $C = A \times B$ is a fundamental routine extensively used in domains like machine learning or graph analytics. Despite its relevance, the efficient execution of SpGEMM on vector…
We propose a new sparse matrix format, PackSELL, designed to support diverse data representations and enable efficient sparse matrix-vector multiplication (SpMV) on GPUs. Building on sliced ELLPACK (SELL), PackSELL incorporates delta…
Specialized computational units that perform small matrix multiplications as primitive operations are typically present in modern AI accelerators. However, these Matrix Multiplication Units (MMUs) are often underutilized for many…
The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the…
Homomorphic encryption (HE) enables computation over encrypted data but incurs a substantial overhead. For sparse-matrix vector multiplication, the widely used Halevi and Shoup (2014) scheme has a cost linear in the number of occupied…
Sparse matrices and linear algebra are at the heart of scientific simulations. More than 70 sparse matrix storage formats have been developed over the years, targeting a wide range of hardware architectures and matrix types. Each format is…
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…
In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…
The Variable Block Row (VBR) format is an influential blocked sparse matrix format designed for matrices with shared sparsity structure between adjacent rows and columns. VBR groups adjacent rows and columns, storing the resulting blocks…
We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it…