Related papers: Directional H2-matrix compression for high-frequen…
We consider the use of multipreconditioning, which allows for multiple preconditioners to be applied in parallel, on high-frequency Helmholtz problems. Typical applications present challenging sparse linear systems which are complex…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…
Rank deficient Hankel matrices are at the core of several applications. However, in practice, the coefficients of these matrices are noisy due to e.g. measurements errors and computational errors, so generically the involved matrices are…
In this paper, we consider the matrices approximated in H2 format. The direct solution, as well as the preconditioning, of systems with such matrices is a challenging problem. We propose a non-extensive sparse factorization of the H2 matrix…
Microstructure reconstruction and compression techniques are designed to find a microstructure with desired properties. While the microstructure reconstruction searches for a microstructure with prescribed statistical properties, the…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
The future of high-performance computing, specifically on future Exascale computers, will presumably see memory capacity and bandwidth fail to keep pace with data generated, for instance, from massively parallel partial differential…
We present and analyze an approximation scheme for a class of highly oscillatory kernel functions, taking the 2D and 3D Helmholtz kernels as examples. The scheme is based on polynomial interpolation combined with suitable pre- and…
Kernel matrices are ubiquitous in computational mathematics, often arising from applications in machine learning and scientific computing. In two or three spatial or feature dimensions, such problems can be approximated efficiently by a…
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…
We consider the efficient solution of strongly elliptic partial differential equations with random load based on the finite element method. The solution's two-point correlation can efficiently be approximated by means of an…
An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal…
In this paper we present an overview of recent progress on the development and analysis of domain decomposition preconditioners for discretised Helmholtz problems, where the preconditioner is constructed from the corresponding problem with…
Despite their high accuracy, complex neural networks demand significant computational resources, posing challenges for deployment on resource constrained devices such as mobile phones and embedded systems. Compression algorithms have been…
Reduced-order models are essential tools to deal with parametric problems in the context of optimization, uncertainty quantification, or control and inverse problems. The set of parametric solutions lies in a low-dimensional manifold (with…
Network compression is crucial to making the deep networks to be more efficient, faster, and generalizable to low-end hardware. Current network compression methods have two open problems: first, there lacks a theoretical framework to…
Many data-fitting applications require the solution of an optimization problem involving a sum of large number of functions of high dimensional parameter. Here, we consider the problem of minimizing a sum of $n$ functions over a convex…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…
Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…