相关论文: Analysis of probing techniques for sparse approxim…

For the Poisson equation posed in a domain containing a large number of polygonal perforations, we propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain. Similarly to other multiscale…

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…

Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For $\alpha \leq 1$ and $k \in \mathbb{Z}^+$, we say that a graph $G=(V,E)$ is…

In the present note we consider a type of matrices stemming in the context of the numerical approximation of distributed order fractional differential equations (FDEs): from one side they could look standard, since they are, real, symmetric…

Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g.,…

In this paper, we consider the mixture of sparse linear regressions model. Let ${\beta}^{(1)},\ldots,{\beta}^{(L)}\in\mathbb{C}^n$ be $ L $ unknown sparse parameter vectors with a total of $ K $ non-zero coefficients. Noisy linear…

Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…

We derive an augmented Krylov subspace method with subspace recycling for computing a sequence of matrix function applications on a set of vectors. The matrix is either fixed or changes as the sequence progresses. We assume consecutive…

A sparse matrix is called double irregular sparse if it has at least one relatively dense column and row, and it is double regular sparse if all the columns and rows of it are sparse. The sparse approximate inverse preconditioning…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods,…

Low-precision computing is essential for efficiently utilizing memory bandwidth and computing cores. While many mixed-precision algorithms have been developed for iterative sparse linear solvers, effectively leveraging half-precision (fp16)…

Sparse approximation is important in many applications because of concise form of an approximant and good accuracy guarantees. The theory of compressed sensing, which proved to be very useful in the image processing and data sciences, is…

The aim of sparse approximation is to estimate a sparse signal according to the measurement matrix and an observation vector. It is widely used in data analytics, image processing, and communication, etc. Up to now, a lot of research has…

We discuss a method for sparse signal approximation, which is based on the correlation of the target signal with a pseudo-random signal, and uses a modification of the greedy matching pursuit algorithm. We show that this approach provides…

This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…

We study efficient algorithms for Sparse PCA in standard statistical models (spiked covariance in its Wishart form). Our goal is to achieve optimal recovery guarantees while being resilient to small perturbations. Despite a long history of…

Subspace tracking is a fundamental problem in signal processing, where the goal is to estimate and track the underlying subspace that spans a sequence of data streams over time. In high-dimensional settings, data samples are often corrupted…

This paper presents two new augmented flexible (AF)-Krylov subspace methods, AF-GMRES and AF-LSQR, to compute solutions of large-scale linear discrete ill-posed problems that can be modeled as the sum of two independent random variables,…

Speculative decoding accelerates autoregressive language model inference by verifying multiple draft tokens in parallel. However, the verification stage often becomes the dominant computational bottleneck, especially for long-context inputs…