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We introduce a new algorithm and software for solving linear equations in symmetric diagonally dominant matrices with non-positive off-diagonal entries (SDDM matrices), including Laplacian matrices. We use pre-conditioned conjugate gradient…

Numerical Analysis · Mathematics 2023-06-16 Yuan Gao , Rasmus Kyng , Daniel A. Spielman

In modern large-scale distributed systems, analytics jobs submitted by various users often share similar work, for example scanning and processing the same subset of data. Instead of optimizing jobs independently, which may result in…

Databases · Computer Science 2018-05-23 Pietro Michiardi , Damiano Carra , Sara Migliorini

Large classes of materials systems in physics and engineering are governed by magnetic and electrostatic interactions. Continuum or mesoscale descriptions of such systems can be cast in terms of integral equations, whose direct…

Computational Physics · Physics 2016-08-15 Xikai Jiang , Jiyuan Li , Xujun Zhao , Jian Qin , Dmitry Karpeev , Juan Hernandez-Ortiz , Juan de Pablo , Olle Heinonen

This report investigates the performance of the JOREK code on the Intel Knights Landing and Skylake processor architectures. The OpenMP scaling of the matrix construction part of the code was analyzed and improved synchronization methods…

Performance · Computer Science 2018-10-11 T. B. Fehér , M. Hölzl , G. Latu , G. T. A. Huijsmans

Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…

Machine Learning · Computer Science 2014-09-04 Fanhua Shang , Yuanyuan Liu , Hanghang Tong , James Cheng , Hong Cheng

In this paper, an exact method is proposed to optimize two fractional linear functions over the efficient set of a fractional multiobjective linear problem (MOILFP). This type of problems is encountered when there are two decision makers…

Optimization and Control · Mathematics 2020-03-12 Yacine Chaiblaine , Mustapha Moulaï , Yasmine Cherfaoui

Given a sparse matrix $A$, the selected inversion algorithm is an efficient method for computing certain selected elements of $A^{-1}$. These selected elements correspond to all or some nonzero elements of the LU factors of $A$. In many…

Mathematical Software · Computer Science 2016-04-12 Mathias Jacquelin , Lin Lin , Weile Jia , Yonghua Zhao , Chao Yang

Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the…

Machine Learning · Computer Science 2023-11-07 Mengyuan Zhang , Kai Liu

We study the problem of scheduling $n$ independent moldable tasks on $m$ processors that arises in large-scale parallel computations. When tasks are monotonic, the best known result is a $(\frac{3}{2}+\epsilon)$-approximation algorithm for…

Data Structures and Algorithms · Computer Science 2023-03-30 Xiaohu Wu , Patrick Loiseau

Despite the various research initiatives and proposed programming models, efficient solutions for parallel programming in HPC clusters still rely on a complex combination of different programming models (e.g., OpenMP and MPI), languages…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-08-16 Hervé Yviquel , Marcio Pereira , Emílio Francesquini , Guilherme Valarini , Gustavo Leite , Pedro Rosso , Rodrigo Ceccato , Carla Cusihualpa , Vitoria Dias , Sandro Rigo , Alan Souza , Guido Araujo

We provide more technical details about the HLIBCov package, which is using parallel hierarchical ($\H$-) matrices to identify unknown parameters of the covariance function (variance, smoothness, and covariance length). These parameters are…

Computation · Statistics 2019-05-02 Alexander Litvinenko

In inverting large sparse matrices, the key difficulty lies in effectively exploiting sparsity during the inversion process. One well-established strategy is the nested dissection, which seeks the so-called sparse Cholesky factorization. We…

Numerical Analysis · Mathematics 2025-05-14 Michał Kos , Krzysztof Podgórski , Hanqing Wu

Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…

Machine Learning · Computer Science 2014-10-24 Jingbo Shang , Tianqi Chen , Hang Li , Zhengdong Lu , Yong Yu

We investigate task clustering for deep-learning based multi-task and few-shot learning in a many-task setting. We propose a new method to measure task similarities with cross-task transfer performance matrix for the deep learning scenario.…

Machine Learning · Computer Science 2018-05-21 Mo Yu , Xiaoxiao Guo , Jinfeng Yi , Shiyu Chang , Saloni Potdar , Gerald Tesauro , Haoyu Wang , Bowen Zhou

We introduce a randomized algorithm, namely RCHOL, to construct an approximate Cholesky factorization for a given Laplacian matrix (a.k.a., graph Laplacian). From a graph perspective, the exact Cholesky factorization introduces a clique in…

Numerical Analysis · Mathematics 2021-09-06 Chao Chen , Tianyu Liang , George Biros

We consider the least-squares approximation of a matrix C in the set of doubly stochastic matrices with the same sparsity pattern as C. Our approach is based on applying the well-known Alternating Direction Method of Multipliers (ADMM) to a…

Optimization and Control · Mathematics 2019-10-14 Nikitas Rontsis , Paul J. Goulart

If a tensor with various symmetries is properly unfolded, then the resulting matrix inherits those symmetries. As tensor computations become increasingly important it is imperative that we develop efficient structure preserving methods for…

Numerical Analysis · Computer Science 2014-12-01 Charles Van Loan , Joseph Vokt

A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…

Numerical Analysis · Mathematics 2019-12-12 Joscha Reimer

Performing Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances, as well as estimating model hyperparameters. Although direct matrix factorizations…

Computation · Statistics 2026-03-17 Abylay Zhumekenov , Elias T. Krainski , Håvard Rue

We present a programming methodology and runtime performance case study comparing the declarative data flow coordination language S-Net with Intel's Concurrent Collections (CnC). As a coordination language S-Net achieves a near-complete…

Programming Languages · Computer Science 2014-04-04 Pavel Zaichenkov , Bert Gijsbers , Clemens Grelck , Olga Tveretina , Alex Shafarenko