Related papers: State-of-The-Art Sparse Direct Solvers

We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…

Despite strong empirical performance for image classification, deep neural networks are often regarded as ``black boxes'' and they are difficult to interpret. On the other hand, sparse convolutional models, which assume that a signal can be…

Sparse linear systems are typically solved using preconditioned iterative methods, but applying preconditioners via sparse triangular solves introduces bottlenecks due to irregular memory accesses and data dependencies. This work leverages…

Fully sparse 3D detection has attracted an increasing interest in the recent years. However, the sparsity of the features in these frameworks challenges the generation of proposals because of the limited diffusion process. In addition, the…

Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must…

Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…

Machine learning is increasingly used to improve decisions within branch-and-bound algorithms for mixed-integer programming. Many existing approaches rely on deep learning, which often requires very large training datasets and substantial…

Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual…

A new sparse SOS decomposition algorithm is proposed based on a new sparsity pattern, called cross sparsity patterns. The new sparsity pattern focuses on the sparsity of terms and thus is different from the well-known correlative sparsity…

This paper proposes a bootstrap-assisted procedure to conduct simultaneous inference for high dimensional sparse linear models based on the recent de-sparsifying Lasso estimator (van de Geer et al. 2014). Our procedure allows the dimension…

This paper provides a novel approach for finding sparse state-space realizations of linear systems (e.g., controllers). Sparse controllers are commonly used in distributed control, where a controller is synthesized with some sparsity…

The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm…

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the…

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…

The multiplication of a sparse matrix with a dense vector (SpMV) is a key component in many numerical schemes and its performance is known to be severely limited by main memory access. Several numerical schemes require the multiplication of…

After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an…

Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…

This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing,…

Most numerical solvers and libraries nowadays are implemented to use mathematical models created with language-specific built-in data types (e.g. real in Fortran or double in C) and their respective elementary algebra implementations.…

In this paper, we propose an adaptive sieving (AS) strategy for solving general sparse machine learning models by effectively exploring the intrinsic sparsity of the solutions, wherein only a sequence of reduced problems with much smaller…