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We propose a convenient matrix-free neural architecture for the multigrid method. The architecture is simple enough to be implemented in less than fifty lines of code, yet it encompasses a large number of distinct multigrid solvers. We…
Given a zero-dimensional ideal I in K[x1,...,xn] of degree D, the transformation of the ordering of its Groebner basis from DRL to LEX is a key step in polynomial system solving and turns out to be the bottleneck of the whole solving…
In recent years, a variety of randomized constructions of sketching matrices have been devised, that have been used in fast algorithms for numerical linear algebra problems, such as least squares regression, low-rank approximation, and the…
We introduce a generic framework for solving linear programs (LPs) with many constraints $(n \gg d)$ via adaptive sparsification. Our approach provides a principled generalization of the techniques of [Assadi '23] from matching problems to…
We present a C++ header-only parallel sparse matrix library, based on sparse quadtree representation of matrices using the Chunks and Tasks programming model. The library implements a number of sparse matrix algorithms for distributed…
This article deals with the computation of the characteristic polynomial of dense matrices over small finite fields and over the integers. We first present two algorithms for the finite fields: one is based on Krylov iterates and Gaussian…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
A major challenge in the deployment of scientific software solutions is the adaptation of research prototypes to production-grade code. While high-level languages like MATLAB are useful for rapid prototyping, they lack the resource…
It is well known that Strassen and Winograd algorithms can reduce the computational costs associated with dense matrix multiplication. We have already shown that they are also very effective for software-based multiple precision…
We present an easy to use and flexible grid library for developing highly scalable parallel simulations. The distributed cartesian cell-refinable grid (dccrg) supports adaptive mesh refinement and allows an arbitrary C++ class to be used as…
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…
The resurgence of machine learning has increased the demand for high-performance basic linear algebra subroutines (BLAS), which have long depended on libraries to achieve peak performance on commodity hardware. High-performance BLAS…
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…
Finite field multiplier is mainly used in error-correcting codes and signal processing. Finite field multiplier is regarded as the bottleneck arithmetic unit for such applications and it is the most complicated operation over finite field…
Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…
We present an optimized single-precision implementation of the Sparse Approximate Matrix Multiply (\SpAMM{}) [M. Challacombe and N. Bock, arXiv {\bf 1011.3534} (2010)], a fast algorithm for matrix-matrix multiplication for matrices with…
Modern sparse language models typically achieve sparsity through Mixture-of-Experts (MoE) layers, which dynamically route tokens to dense MLP "experts." However, dynamic hard routing has a number of drawbacks, such as potentially poor…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
Linear algebra operations have been widely used in big data analytics and scientific computations. Many works have been done on optimizing linear algebra operations on GPUs with regular-shaped input. However, few works focus on fully…
Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…