Related papers: Implementing Communication-Optimal Parallel and Se…

The Cholesky QR algorithm is an efficient communication-minimizing algorithm for computing the QR factorization of a tall-skinny matrix. Unfortunately it has the inherent numerical instability and breakdown when the matrix is…

We implement two novel algorithms for sparse-matrix dense-matrix multiplication (SpMM) on the GPU. Our algorithms expect the sparse input in the popular compressed-sparse-row (CSR) format and thus do not require expensive format conversion.…

We are interested in parallelizing the Least Angle Regression (LARS) algorithm for fitting linear regression models to high-dimensional data. We consider two parallel and communication avoiding versions of the basic LARS algorithm. The two…

This article proposes and analyzes several variants of the randomized Cholesky QR factorization of a matrix $X$. Instead of computing the R factor from $X^T X$, as is done by standard methods, we obtain it from a small, efficiently…

General matrix-matrix multiplications with double-precision real and complex entries (DGEMM and ZGEMM) in vendor-supplied BLAS libraries are best optimized for square matrices but often show bad performance for tall & skinny matrices, which…

We propose two new methods to address the weak scaling problems of KRR: the Balanced KRR (BKRR) and K-means KRR (KKRR). These methods consider alternative ways to partition the input dataset into p different parts, generating p different…

This paper proposes a scalable binary CUR low-rank approximation algorithm that leverages parallel selection of representative rows and columns within a deterministic framework. By employing a blockwise adaptive cross approximation…

As quantum computers continue to improve and support larger, more complex computations, smart control hardware and compilers are needed to efficiently leverage the capabilities of these systems. This paper introduces a novel approach to…

This paper presents an efficient parallel approximation scheme for a new class of min-max problems. The algorithm is derived from the matrix multiplicative weights update method and can be used to find near-optimal strategies for…

We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…

This paper presents a fault-tolerant algorithm for the QR factorization of general matrices. It relies on the communication-avoiding algorithm, and uses the structure of the reduction of each part of the computation to introduce…

This paper introduces hybrid LU-QR al- gorithms for solving dense linear systems of the form Ax = b. Throughout a matrix factorization, these al- gorithms dynamically alternate LU with local pivoting and QR elimination steps, based upon…

Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…

We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single…

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…

Sparse matrix multiplication is an important component of linear algebra computations. In this paper, an architecture based on Content Addressable Memory (CAM) and Resistive Content Addressable Memory (ReCAM) is proposed for accelerating…

Computing fixed-radius near-neighbor graphs is an important first step for many data analysis algorithms. Near-neighbor graphs connect points that are close under some metric, endowing point clouds with a combinatorial structure. As…

This article introduces a highly parallel algorithm for molecular dynamics simulations with short-range forces on single node multi- and many-core systems. The algorithm is designed to achieve high parallel speedups for strongly…

We demonstrate an implementation for an approximate rank-k SVD factorization, combining well-known randomized projection techniques with previously known paralel solutions in order to compute steps of the random projection based SVD…

The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…