Related papers: A DEIM-CUR factorization with iterative SVDs

In this paper, we focus on the reduced basis methodology in the context of non-linear non-affinely parametrized partial differential equations in which affine decomposition necessary for the reduced basis methodology are not obtained [4,…

We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…

The incremental singular value decomposition (SVD) updates a truncated SVD as new columns arrive, replacing a single large SVD with a sequence of small ones. In floating-point arithmetic, each update multiplies the running singular basis by…

A new algorithm to compute the restricted singular value decomposition of dense matrices is presented. Like Zha's method \cite{Zha92}, the new algorithm uses an implicit Kogbetliantz iteration, but with four major innovations. The first…

Clustering is often used for discovering structure in data. Clustering systems differ in the objective function used to evaluate clustering quality and the control strategy used to search the space of clusterings. Ideally, the search…

Robust principal component analysis (RPCA) is a widely used tool for dimension reduction. In this work, we propose a novel non-convex algorithm, coined Iterated Robust CUR (IRCUR), for solving RPCA problems, which dramatically improves the…

We introduce meta-factorization, a theory that describes matrix decompositions as solutions of linear matrix equations: the projector and the reconstruction equation. Meta-factorization reconstructs known factorizations, reveals their…

A CUR approximation of a matrix $A$ is a particular type of low-rank approximation $A \approx C U R$, where $C$ and $R$ consist of columns and rows of $A$, respectively. One way to obtain such an approximation is to apply column subset…

Bayesian statistical inverse problems are often solved with Markov chain Monte Carlo (MCMC)-type schemes. When the problems are governed by large-scale discrete nonlinear partial differential equations (PDEs), they are computationally…

The tensor Singular Value Decomposition (t-SVD) for third order tensors that was proposed by Kilmer and Martin~\cite{2011kilmer} has been applied successfully in many fields, such as computed tomography, facial recognition, and video…

Integral equations are commonly encountered when solving complex physical problems. Their discretization leads to a dense kernel matrix that is block or hierarchically low-rank. This paper proposes a new way to build a low-rank…

The Nystr\"{o}m method is routinely used for out-of-sample extension of kernel matrices. We describe how this method can be applied to find the singular value decomposition (SVD) of general matrices and the eigenvalue decomposition (EVD) of…

A low-rank approximation of a parameter-dependent matrix $A(t)$ is an important task in the computational sciences appearing for example in dynamical systems and compression of a series of images. In this work, we introduce AdaCUR, an…

The Singular Value Decomposition (SVD) is one of the most important matrix factorizations, enjoying a wide variety of applications across numerous application domains. In statistics and data analysis, the common applications of SVD such as…

Simulations of large scale dynamical systems in multi-query or real-time contexts require efficient surrogate modelling techniques, as e.g. achieved via Model Order Reduction (MOR). Recently, symplectic methods like the complex singular…

We develop an iterative subsampling approach to improve the computational efficiency of our previous work on solution path clustering (SPC). The SPC method achieves clustering by concave regularization on the pairwise distances between…

Dynamical low-rank approximation allows for solving large-scale matrix differential equations (MDEs) with significantly fewer degrees of freedom and has been applied to a growing number of applications. However, most existing techniques…

Symmetric positive semi-definite (SPSD) matrix approximation methods have been extensively used to speed up large-scale eigenvalue computation and kernel learning methods. The standard sketch based method, which we call the prototype model,…

This paper presents a multi-field decomposed approach for hyper-reduced order modeling to overcome the limitations of traditional model reduction techniques for gradient-extended damage-plasticity simulations. The discrete empirical…

Invariant Coordinate Selection (ICS) is a multivariate data transformation and a dimension reduction method that can be useful in many different contexts. It can be used for outlier detection or cluster identification, and can be seen as an…