Related papers: A DEIM-CUR factorization with iterative SVDs
Modelling of physical systems may be a challenging task when it requires solving large sets of numerical equations. This is the case of photovoltaic (PV) systems which contain many PV modules, each module containing several silicon cells.…
Accurate simulations are essential for engineering applications, and intricate continuum mechanical material models are constructed to achieve this goal. However, the increasing complexity of the material models and geometrical properties…
This article discusses a useful tool in dimensionality reduction and low-rank matrix approximation called the CUR decomposition. Various viewpoints of this method in the literature are synergized and are compared and contrasted; included in…
Manifold learning techniques seek to discover structure-preserving mappings of high-dimensional data into low-dimensional spaces. While the new sets of coordinates specified by these mappings can closely parameterize the data, they are…
This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality…
Singular value decomposition (SVD) is a standard matrix factorization technique that produces optimal low-rank approximations of matrices. It has diverse applications, including machine learning, data science and signal processing. However,…
In this paper, we propose a new coded computing technique called "substitute decoding" for general iterative distributed computation tasks. In the first part of the paper, we use PageRank as a simple example to show that substitute decoding…
CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for…
Data-aware methods for dimensionality reduction and matrix decomposition aim to find low-dimensional structure in a collection of data. Classical approaches discover such structure by learning a basis that can efficiently express the…
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…
This paper aims to develop a simple procedure to reduce and control the condition number of random matrices, and investigate the effect on the persistent homology (PH) of point clouds of well- and ill-conditioned matrices. For a square…
We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the…
Traditional low-rank approximation is a powerful tool to compress the huge data matrices that arise in simulations of partial differential equations (PDE), but suffers from high computational cost and requires several passes over the PDE…
In this paper, we propose a probabilistic model for computing an interpolative decomposition (ID) in which each column of the observed matrix has its own priority or importance, so that the end result of the decomposition finds a set of…
Developing efficient solvers for large-scale multi-term linear matrix equations remains a central challenge in numerical linear algebra and is still largely unresolved. This paper introduces a methodology leveraging CUR decomposition for…
Prior optimal CUR decomposition and near optimal column reconstruction methods have been established by combining BSS sampling and adaptive sampling. In this paper, we propose a new approach to the optimal CUR decomposition and near optimal…
The factorization of three-dimensional data continues to gain attention due to its relevance in representing and compressing large-scale datasets. The linear-map-based tensor-tensor multiplication is a matrix-mimetic operation that extends…
In the field of model predictive control, Data-enabled Predictive Control (DeePC) offers direct predictive control, bypassing traditional modeling. However, challenges emerge with increased computational demand due to recursive data…
This article studies how to form CUR decompositions of low-rank matrices via primarily random sampling, though deterministic methods due to previous works are illustrated as well. The primary problem is to determine when a column submatrix…
Column selection is an essential tool for structure-preserving low-rank approximation, with wide-ranging applications across many fields, such as data science, machine learning, and theoretical chemistry. In this work, we develop unified…