Related papers: parGeMSLR: A Parallel Multilevel Schur Complement …

Gaussian processes (GPs) stand as crucial tools in machine learning and signal processing, with their effectiveness hinging on kernel design and hyper-parameter optimization. This paper presents a novel GP linear multiple kernel (LMK) and a…

Sparse matrix multiplication (SpGEMM) is a fundamental kernel used in many diverse application areas, both numerical and discrete. For example, many algebraic graph algorithms rely on SpGEMM in the tropical semiring to compute shortest…

Sparse matrix vector multiplication (SpMV) is a fundamental kernel in scientific codes that rely on iterative solvers. In this first part of our work, we present both a sequential and a basic MPI parallel implementations of SpMV, aiming to…

The class of quasiseparable matrices is defined by the property that any submatrix entirely below or above the main diagonal has small rank, namely below a bound called the order of quasiseparability. These matrices arise naturally in…

In this paper, we consider an approach to the parallelizing of the algorithms realizing the modified probability changigng method with adaptation and partial rollback procedure for constrained pseudo-Boolean optimization problems. Existing…

We present GSPMD, an automatic, compiler-based parallelization system for common machine learning computations. It allows users to write programs in the same way as for a single device, then give hints through a few annotations on how to…

In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…

There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…

Nonnegative least squares problems with multiple right-hand sides (MNNLS) arise in models that rely on additive linear combinations. In particular, they are at the core of most nonnegative matrix factorization algorithms and have many…

The emergence of low precision floating-point arithmetic in computer hardware has led to a resurgence of interest in the use of mixed precision numerical linear algebra. For linear systems of equations, there has been renewed enthusiasm for…

Designing and implementing efficient, provably correct parallel machine learning (ML) algorithms is challenging. Existing high-level parallel abstractions like MapReduce are insufficiently expressive while low-level tools like MPI and…

Designing and implementing efficient, provably correct parallel machine learning (ML) algorithms is challenging. Existing high-level parallel abstractions like MapReduce are insufficiently expressive while low-level tools like MPI and…

We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…

With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…

General sparse matrix-matrix multiplication (SpGEMM) is an integral part of many scientific computing, high-performance computing (HPC), and graph analytic applications. This paper presents a new compressed sparse vector (CSV) format for…

The recently developed semi-Lagrangian discontinuous Galerkin approach is used to discretize hyperbolic partial differential equations (usually first order equations). Since these methods are conservative, local in space, and able to limit…

Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…

Sparse plus Low-Rank $(\mathbf{S} + \mathbf{LR})$ decomposition of Large Language Models (LLMs) has emerged as a promising direction in model compression, aiming to decompose pre-trained model weights into a sum of sparse and low-rank…

In this work, we present a new scalable incomplete LU factorization framework called Javelin to be used as a preconditioner for solving sparse linear systems with iterative methods. Javelin allows for improved parallel factorization on…

In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…