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Calculation of near-neighbor interactions among high dimensional, irregularly distributed data points is a fundamental task to many graph-based or kernel-based machine learning algorithms and applications. Such calculations, involving…

Large-scale machine learning (ML) models are increasingly being used in critical domains like education, lending, recruitment, healthcare, criminal justice, etc. However, the training, deployment, and utilization of these models demand…

Machine Learning · Computer Science 2025-03-31 Ding Zhu , Zhiqun Zuo , Mohammad Mahdi Khalili

Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…

Numerical Analysis · Mathematics 2019-05-24 Minhong Chen , Daniel Kressner

Subspace clustering (SC) is a popular method for dimensionality reduction of high-dimensional data, where it generalizes Principal Component Analysis (PCA). Recently, several methods have been proposed to enhance the robustness of PCA and…

Data Structures and Algorithms · Computer Science 2015-06-09 Sanghyuk Chun , Yung-Kyun Noh , Jinwoo Shin

The tremendous increase in the size and heterogeneity of supercomputers makes it very difficult to predict the performance of a scheduling algorithm. Therefore, dynamic solutions, where scheduling decisions are made at runtime have…

Distributed, Parallel, and Cluster Computing · Computer Science 2014-04-16 Olivier Beaumont , Loris Marchal

A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths…

Numerical Analysis · Mathematics 2019-07-05 Juan A. Acebron , Jose R. Herrero , Jose Monteiro

Iterative solvers are frequently used in scientific applications and engineering computations. However, the memory-bound Sparse Matrix-Vector (SpMV) kernel computation hinders the efficiency of iterative algorithms. As modern hardware…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-11-08 Jianhua Gao , Jiayuan Shen , Yuxiang Zhang , Weixing Ji , Hua Huang

We consider discretizations of the hyper-singular integral operator on closed surfaces and show that the inverses of the corresponding system matrices can be approximated by blockwise low-rank matrices at an exponential rate in the block…

Numerical Analysis · Mathematics 2017-12-04 Markus Faustmann , Jens Markus Melenk , Dirk Praetorius

The advent of memristive devices offers a promising avenue for efficient and scalable analog computing, particularly for linear algebra operations essential in various scientific and engineering applications. This paper investigates the…

Mesoscale and Nanoscale Physics · Physics 2025-06-23 Jonathan Lin , Frank Barrows , Francesco Caravelli

We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…

Numerical Analysis · Mathematics 2022-08-15 Chao Chen , Per-Gunnar Martinsson

Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-01-08 Austin R. Benson , Grey Ballard

We present Accelerated Cyclic Reduction (ACR), a distributed-memory fast direct solver for rank-compressible block tridiagonal linear systems arising from the discretization of elliptic operators, developed here for three dimensions.…

Analysis of PDEs · Mathematics 2018-01-08 Gustavo Chávez , George Turkiyyah , Stefano Zampini , Hatem Ltaief , David Keyes

Multiplication is a fundamental operation in many applications, and multipliers are widely adopted in various circuits. However, optimizing multipliers is challenging due to the extensive design space. In this paper, we propose a multiplier…

Hardware Architecture · Computer Science 2024-12-30 Dongsheng Zuo , Jiadong Zhu , Yikang Ouyang , Yuzhe Ma

This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…

Numerical Analysis · Mathematics 2025-02-05 Lucas Onisk , Malena Sabaté Landman

We introduce Stream-K, a work-centric parallelization of matrix multiplication (GEMM) and related computations in dense linear algebra. Whereas contemporary decompositions are primarily tile-based, our method operates by partitioning an…

Data Structures and Algorithms · Computer Science 2023-01-11 Muhammad Osama , Duane Merrill , Cris Cecka , Michael Garland , John D. Owens

The paper describes several efficient parallel implementations of the one-sided hyperbolic Jacobi-type algorithm for computing eigenvalues and eigenvectors of Hermitian matrices. By appropriate blocking of the algorithms an almost ideal…

Numerical Analysis · Computer Science 2020-03-18 Sanja Singer , Sasa Singer , Vedran Novakovic , Davor Davidovic , Kresimir Bokulic , Aleksandar Uscumlic

In this paper we study fast iterative solvers for the large sparse linear systems resulting from the stochastic Galerkin discretization of stochastic partial differential equations. A block triangular preconditioner is introduced and…

Numerical Analysis · Mathematics 2013-04-08 Bin Zheng , Guang Lin , Jinchao Xu

We study the two-dimensional hierarchical rectangle packing problem, motivated by applications in analog integrated circuit layout, facility layout, and logistics. Unlike classical strip or bin packing, the dimensions of the container are…

Computational Geometry · Computer Science 2025-12-24 Josef Grus , Zdeněk Hanzálek , Christian Artigues , Cyrille Briand , Emmanuel Hebrard

Use of the stochastic Galerkin finite element methods leads to large systems of linear equations obtained by the discretization of tensor product solution spaces along their spatial and stochastic dimensions. These systems are typically…

Numerical Analysis · Mathematics 2014-07-17 Bedřich Sousedík , Roger G. Ghanem , Eric T. Phipps

In-memory columnar databases have become mainstream over the last decade and have vastly improved the fast processing of large volumes of data through multi-core parallelism and in-memory compression thereby eliminating the usual…

Databases · Computer Science 2016-09-27 Jayanth Jayanth