Related papers: hm-toolbox: Matlab software for HODLR and HSS matr…
This article introduces HODLR3D, a class of hierarchical matrices arising out of $N$-body problems in three dimensions. HODLR3D relies on the fact that certain off-diagonal matrix sub-blocks arising out of the $N$-body problems in three…
HOTTBOX is a Python library for exploratory analysis and visualisation of multi-dimensional arrays of data, also known as tensors. The library includes methods ranging from standard multi-way operations and data manipulation through to…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
Factorization of large dense matrices are ubiquitous in engineering and data science applications, e.g. preconditioners for iterative boundary integral solvers, frontal matrices in sparse multifrontal solvers, and computing the determinant…
The efficient and accurate QR decomposition for matrices with hierarchical low-rank structures, such as HODLR and hierarchical matrices, has been challenging. Existing structure-exploiting algorithms are prone to numerical instability as…
In this work, we consider the reformulation of hierarchical ($\mathcal{H}$) matrix algorithms for many-core processors with a model implementation on graphics processing units (GPUs). $\mathcal{H}$ matrices approximate specific dense…
The aim of this work is to develop a fast algorithm for approximating the matrix function $f(A)$ of a square matrix $A$ that is symmetric and has hierarchically semiseparable (HSS) structure. Appearing in a wide variety of applications,…
Hierarchical least-squares programming (HLSP) is an important tool in optimization as it enables the stacking of any number of priority levels in order to reflect complex constraint relationships, for example in physical systems like…
In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…
In the 20th century, newly invented technical artifacts were connected to form large-scale complex engineering systems. Furthermore, the interactions found within these networked systems has grown in both degree as well as heterogeneity.…
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Hierarchical matrices provide a highly memory-efficient way of storing dense linear operators arising, for example, from boundary element methods, particularly when stored in the H^2 format. In such data-sparse representations, iterative…
The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations that, in principle, offers an exponential improvement in scaling with the system size compared to classical approaches. In this work,…
Inversion of sparse matrices with standard direct solve schemes is robust, but computationally expensive. Iterative solvers, on the other hand, demonstrate better scalability; but, need to be used with an appropriate preconditioner (e.g.,…
Solving linear systems of equations plays a fundamental role in numerous computational problems from different fields of science. The widespread use of numerical methods to solve these systems motivates investigating the feasibility of…
In recent years, aerial platforms have evolved from passive flying sensors into versatile, contact-aware robotic systems, leading to rapid advances in platform design. Standard coplanar and collinear quadrotors have been complemented by…
For reconstruction of low-rank matrices from undersampled measurements, we develop an iterative algorithm based on least-squares estimation. While the algorithm can be used for any low-rank matrix, it is also capable of exploiting a-priori…
This paper introduces HALLaR, a new first-order method for solving large-scale semidefinite programs (SDPs) with bounded domain. HALLaR is an inexact augmented Lagrangian (AL) method where the AL subproblems are solved by a novel hybrid…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…