相关论文: Adaptive Algebraic Reuse of Reordering in Cholesky…

The description of weakly bound electronic states is especially difficult with atomic orbital basis sets. The diffuse atomic basis functions that are necessary to describe the extended electronic state generate significant linear…

High-dimensional sparse data emerge in many critical application domains such as healthcare and cybersecurity. To extract meaningful insights from massive volumes of these multi-dimensional data, scientists employ unsupervised analysis…

This paper introduces a fast algorithm for simultaneous inversion and determinant computation of small sized matrices in the context of fully Polarimetric Synthetic Aperture Radar (PolSAR) image processing and analysis. The proposed fast…

The main computational cost of algorithms for computing reduced-order models of parametric dynamical systems is in solving sequences of very large and sparse linear systems. We focus on efficiently solving these linear systems, arising…

We propose a parameter optimization method for achieving static equilibrium of discrete elastic rods. Our method simultaneously optimizes material stiffness and rest shape parameters under box constraints to exactly enforce zero net force…

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 propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that…

Tensors play a vital role in machine learning (ML) and often exhibit properties best explored while maintaining high-order. Efficiently performing ML computations requires taking advantage of sparsity, but generalized hardware support is…

Estimating large covariance matrices has been a longstanding important problem in many applications and has attracted increased attention over several decades. This paper deals with two methods based on pre-existing works to impose sparsity…

Implicit solvers present strong limitations when used on supercomputing facilities and in particular for adaptive mesh-refinement codes. We present a new method for implicit adaptive time-stepping on adaptive mesh refinement-grids. We…

We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…

Many large-scale systems rely on high-quality deep representations (embeddings) to facilitate tasks like retrieval, search, and generative modeling. Matryoshka Representation Learning (MRL) recently emerged as a solution for adaptive…

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…

Recurrence equations lie at the heart of many computational paradigms including dynamic programming, graph analysis, and linear solvers. These equations are often expensive to compute and much work has gone into optimizing them for…

The problem of optimal precision switching for the conjugate gradient (CG) method applied to sparse linear systems is considered. A sparse matrix is defined as an $n\!\times\!n$ matrix with $m\!=\!O(n)$ nonzero entries. The algorithm first…

For many applications involving a sequence of linear systems with slowly changing system matrices, subspace recycling, which exploits relationships among systems and reuses search space information, can achieve huge gains in iterations…

The Cholesky decomposition plays an important role in finding the inverse of the correlation matrices. As it is a fast and numerically stable for linear system solving, inversion, and factorization compared to singular valued decomposition…

Physical systems commonly exhibit spatially varying complexity, presenting a significant challenge for neural PDE solvers. While Graph Neural Networks can handle the irregular meshes required for complex geometries and boundary conditions,…

We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the…

Multi-head-self-attention (MHSA) mechanisms achieve state-of-the-art (SOTA) performance across natural language processing and vision tasks. However, their quadratic dependence on sequence lengths has bottlenecked inference speeds. To…