Related papers: The Eigenvalues Slicing Library (EVSL): Algorithms…
In this paper, we propose an algorithm that can be used on top of a wide variety of self-supervised (SSL) approaches to take advantage of hierarchical structures that emerge during training. SSL approaches typically work through some…
Pattern matching of streaming time series with lower latency under limited computing resource comes to a critical problem, especially as the growth of Industry 4.0 and Industry Internet of Things. However, against traditional single pattern…
The generalized singular value decomposition (GSVD, a.k.a. "SVD triplet", "duality diagram" approach) provides a unified strategy and basis to perform nearly all of the most common multivariate analyses (e.g., principal components,…
Strong gravitational lensing offers a wealth of astrophysical information on the background source it affects, provided the lensed source can be reconstructed as if it was seen in the absence of lensing. In the present work, we illustrate…
Motivation: Surface generation and visualization are some of the most important tasks in biomolecular modeling and computation. Eulerian solvent excluded surface (ESES) software provides analytical solvent excluded surface (SES) in the…
We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which…
Krylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspace provides for estimating the numerical range of a matrix.…
Sparse linear system solvers ($Ax=b$) are critical computational kernels in Electronic Design Automation (EDA), underpinning vital simulations for modern IC and system design. Applications like power integrity verification and…
Spectral clustering has shown a superior performance in analyzing the cluster structure. However, its computational complexity limits its application in analyzing large-scale data. To address this problem, many low-rank matrix approximating…
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…
This paper generalizes the parallel selected inversion algorithm called PSelInv to sparse non- symmetric matrices. We assume a general sparse matrix A has been decomposed as PAQ = LU on a distributed memory parallel machine, where L, U are…
We present the Matlab toolbox MacaulayLab, which implements numerical linear algebra algorithms for solving multivariate polynomial systems and rectangular multiparameter eigenvalue problems. Its structure and functionality are the result…
Applications that need to sense, measure, and gather real-time information from the environment frequently face three main restrictions: power consumption, cost, and lack of infrastructure. Most of the challenges imposed by these…
This note provides a lightweight tutorial on using Eigen, a C++ template library for linear algebra, to implement statistical and machine learning algorithms. The emphasis is practical rather than methodological: we show how common matrix…
We propose a self-supervised machine learning (SSML) framework for multi-fidelity learning and extended predictive soil spectroscopy based on latent space embeddings. A self-supervised representation was pretrained with the large MIR…
Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the…
Log parsing is a fundamental step in log analysis, partitioning raw logs into constant templates and dynamic variables. While recent semantic-based parsers leveraging Large Language Models (LLMs) exhibit superior generalizability over…
One of the problems of producing spectrographs for Extremely Large Telescopes (ELTs) is that the beam size is required to scale with telescope aperture if all other parameters are held constant, leading to enormous size and implied cost.…
Solving dense Hermitian eigenproblems arranged in a sequence with direct solvers fails to take advantage of those spectral properties which are pertinent to the entire sequence, and not just to the single problem. When such features take…
We present a solution to scale spectral algorithms for learning sequence functions. We are interested in the case where these functions are sparse (that is, for most sequences they return 0). Spectral algorithms reduce the learning problem…