Related papers: Low-rank correction methods for algebraic domain d…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.…
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…
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…
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…
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…