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It has been recently shown that incorporating priori knowledge significantly improves the performance of basic compressive sensing based approaches. We have managed to successfully exploit this idea for recovering a matrix as a summation of…

Computer Vision and Pattern Recognition · Computer Science 2014-11-25 Dornoosh Zonoobi , Shahrooz Faghih Roohi , Ashraf A. Kassim

In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…

Numerical Analysis · Mathematics 2026-05-29 Yonghan Sun , Hou-Duo Qi , Deren Han , Jiaxin Xie

Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for…

Numerical Analysis · Mathematics 2022-01-10 Hussam Al Daas , Pierre Jolivet , Tyrone Rees

In this paper, we develop a low-rank method with high-order temporal accuracy using spectral deferred correction (SDC) to compute linear matrix differential equations. In [1], a low rank numerical method is proposed to correct the modeling…

Numerical Analysis · Mathematics 2024-12-13 Shun Li , Yan Jiang , Yingda Cheng

We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…

Machine Learning · Statistics 2023-11-15 Dimitris Bertsimas , Ryan Cory-Wright , Nicholas A. G. Johnson

We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph…

Numerical Analysis · Mathematics 2026-03-11 Stephan Köhler , Oliver Rheinbach , Yue Xiang Tee , Sebastian Zug

A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…

Numerical Analysis · Mathematics 2020-06-09 Simon Arridge , Pascal Fernsel , Andreas Hauptmann

This paper proposes a framework for simultaneous dimensionality reduction and regression in the presence of outliers in data by applying low-rank and sparse matrix decomposition. For multivariate data corrupted with outliers, it is…

Signal Processing · Electrical Eng. & Systems 2024-07-10 Farwa Abbas , Hussain Ahmad

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 propose a computational framework for computing low-rank approximations to the ensemble of solutions of a parametrized system of the form $A(\xi)x(\xi)+g(x(\xi))=b(\xi)$ for multiple parameter values. The central idea is to reinterpret…

Numerical Analysis · Mathematics 2026-04-09 Marco Sutti , Tommaso Vanzan

In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…

Numerical Analysis · Mathematics 2017-05-11 Loic Giraldi , Anthony Nouy , Gregory Legrain

We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness…

Machine Learning · Statistics 2018-02-21 Xiao Zhang , Lingxiao Wang , Quanquan Gu

In this paper, we propose an innovative isogeometric low-rank solver for the linear elasticity model problem, specifically designed to allow multipatch domains. Our approach splits the domain into subdomains, each formed by the union of…

Numerical Analysis · Mathematics 2024-12-17 Monica Montardini , Giancarlo Sangalli , Mattia Tani

Constrained tensor and matrix factorization models allow to extract interpretable patterns from multiway data. Therefore identifiability properties and efficient algorithms for constrained low-rank approximations are nowadays important…

Machine Learning · Computer Science 2022-01-24 Jeremy E. Cohen

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially…

Numerical Analysis · Mathematics 2015-08-13 Daniel Kressner , Michael Steinlechner , Bart Vandereycken

The study deals with the parallelization of finite element based Navier-Stokes codes using domain decomposition and state-ofart sparse direct solvers. There has been significant improvement in the performance of sparse direct solvers.…

Distributed, Parallel, and Cluster Computing · Computer Science 2009-11-05 Mandhapati P. Raju , Siddhartha Khaitan

In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations. Convergence of domain decomposition methods rely…

Numerical Analysis · Mathematics 2021-07-08 Niall Bootland , Victorita Dolean , Frédéric Nataf , Pierre-Henri Tournier

Tensor completion is a challenging problem with various applications. Many related models based on the low-rank prior of the tensor have been proposed. However, the low-rank prior may not be enough to recover the original tensor from the…

Numerical Analysis · Mathematics 2019-11-20 Ping-Ping Wang , Liang Li , Guang-Hui Cheng

The extension of ab initio quantum many-body theory to higher accuracy and larger systems is intrinsically limited by the handling of large data objects in form of wave-function expansions and/or many-body operators. In this work we present…

Nuclear Theory · Physics 2021-09-27 A. Tichai , P. Arthuis , K. Hebeler , M. Heinz , J. Hoppe , A. Schwenk

We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple…

Computer Vision and Pattern Recognition · Computer Science 2015-11-24 Jie Chen , Haixian Zhang , Hua Mao , Yongsheng Sang , Zhang Yi