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The Cholesky decomposition is a fundamental tool for solving linear systems with symmetric and positive definite matrices which are ubiquitous in linear algebra, optimization, and machine learning. Its numerical stability can be improved by…

Machine Learning · Computer Science 2025-07-29 Filip de Roos , Fabio Muratore

The formation trajectory planning using complete graphs to model collaborative constraints becomes computationally intractable as the number of drones increases due to the curse of dimensionality. To tackle this issue, this paper presents a…

Robotics · Computer Science 2024-03-27 Yuan Zhou , Lun Quan , Chao Xu , Guangtong Xu , Fei Gao

We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We…

Optimization and Control · Mathematics 2018-02-22 Thomas Möllenhoff , Zhenzhang Ye , Tao Wu , Daniel Cremers

The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…

Computational Physics · Physics 2015-06-11 Ran Xu , Bin Liu , Yuan Dong

Graph Laplacian learning, also known as network topology inference, is a problem of great interest to multiple communities. In Gaussian graphical models (GM), graph learning amounts to endowing covariance selection with the Laplacian…

Machine Learning · Computer Science 2024-02-14 Changhao Shi , Gal Mishne

The Massively Parallel Computation (MPC) model is an emerging model which distills core aspects of distributed and parallel computation. It has been developed as a tool to solve (typically graph) problems in systems where the input is…

Data Structures and Algorithms · Computer Science 2020-02-20 Artur Czumaj , Peter Davies , Merav Parter

Preconditioning for overdetermined least-squares problems has received comparatively little attention, and designing methods that are both effective and memory-efficient remains challenging. We propose a class of ILU-based preconditioners…

Numerical Analysis · Mathematics 2026-03-31 Jennifer Scott , Miroslav Tůma

Computation of a signal's estimated covariance matrix is an important building block in signal processing, e.g., for spectral estimation. Each matrix element is a sum of products of elements in the input matrix taken over a sliding window.…

Data Structures and Algorithms · Computer Science 2013-03-12 Oded Green , Lior David , Ami Galperin , Yitzhak Birk

Usage of multiprocessor and multicore computers implies parallel programming. Tools for preparing parallel programs include parallel languages and libraries as well as parallelizing compilers and convertors that can perform automatic…

Mathematical Software · Computer Science 2022-12-12 Pavel Telegin , Anton Baranov , Boris Shabanov , Artem Tikhomirov

The increasing complexity of deep learning recommendation models (DLRM) has led to a growing need for large-scale distributed systems that can efficiently train vast amounts of data. In DLRM, the sparse embedding table is a crucial…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-08-07 Xin Zhang , Quanyu Zhu , Liangbei Xu , Zain Huda , Wang Zhou , Jin Fang , Dennis van der Staay , Yuxi Hu , Jade Nie , Jiyan Yang , Chunzhi Yang

In this paper, we study a parallel-in-time (PinT) algorithm for all-at-once system from a non-local evolutionary equation with weakly singular kernel where the temporal term involves a non-local convolution with a weakly singular kernel and…

Numerical Analysis · Mathematics 2021-03-17 Xue-lei Lin , Michael K. Ng , Yajing Zhi

We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…

Numerical Analysis · Mathematics 2018-05-08 Daria A. Sushnikova , Ivan V. Oseledets

Structural clustering is one of the most popular graph clustering methods, which has achieved great performance improvement by utilizing GPUs. Even though, the state-of-the-art GPU-based structural clustering algorithm, GPUSCAN, still…

Databases · Computer Science 2023-12-01 Long Yuan , Zeyu Zhou , Xuemin Lin , Zi Chen , Xiang Zhao , Fan Zhang

This paper proposes efficient solutions for $k$-core decomposition with high parallelism. The problem of $k$-core decomposition is fundamental in graph analysis and has applications across various domains. However, existing algorithms face…

Data Structures and Algorithms · Computer Science 2025-03-25 Youzhe Liu , Xiaojun Dong , Yan Gu , Yihan Sun

Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…

Computational Engineering, Finance, and Science · Computer Science 2019-01-23 Richard Barnes

Prior work on Automatically Scalable Computation (ASC) suggests that it is possible to parallelize sequential computation by building a model of whole-program execution, using that model to predict future computations, and then…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-09-21 Peter Kraft , Amos Waterland , Daniel Y Fu , Anitha Gollamudi , Shai Szulanski , Margo Seltzer

The multilevel Schwarz preconditioner is one of the most popular parallel preconditioners for enhancing convergence and improving parallel efficiency. However, its parallel implementation on arbitrary unstructured triangular/tetrahedral…

Numerical Analysis · Mathematics 2024-12-13 Chengdi Ma

CholeskyQR is a simple and fast QR decomposition via Cholesky decomposition, while it has been considered highly sensitive to the condition number. In this paper, we provide a randomized preconditioner framework for CholeskyQR algorithm.…

Numerical Analysis · Mathematics 2021-11-25 Yuwei Fan , Yixiao Guo , Ting Lin

The ParaDiag family of algorithms solves differential equations by using preconditioners that can be inverted in parallel through diagonalization. In the context of optimal control of linear parabolic PDEs, the state-of-the-art ParaDiag…

Numerical Analysis · Mathematics 2024-03-15 Arne Bouillon , Giovanni Samaey , Karl Meerbergen

The successive projection algorithm (SPA) can quickly solve a nonnegative matrix factorization problem under a separability assumption. Even if noise is added to the problem, SPA is robust as long as the perturbations caused by the noise…

Numerical Analysis · Computer Science 2018-05-11 Tomohiko Mizutani , Mirai Tanaka