Related papers: Memory-efficient compression of $\mathcal{DH}^2$-m…
We consider a compression method for boundary element matrices arising in the context of the computation of electrostatic fields. Green cross approximation combines an analytic approximation of the kernel function based on Green's…
Due to its highly oscillating solution, the Helmholtz equation is numerically challenging to solve. To obtain a reasonable solution, a mesh size that is much smaller than the reciprocal of the wavenumber is typically required (known as the…
The adoption of Transformer-based models in natural language processing (NLP) has led to great success using a massive number of parameters. However, due to deployment constraints in edge devices, there has been a rising interest in the…
Recently Implicit Neural Representations (INRs) gained attention as a novel and effective representation for various data types. Thus far, prior work mostly focused on optimizing their reconstruction performance. This work investigates INRs…
Several researchers have developed a rich toolbox of matrix compression techniques that exploit structure and redundancy in large matrices. Classical methods such as the block low-rank format and the Fast Multipole Method make it possible…
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…
We propose a model reduction technique for parametrized partial differential equations arising from scalar hyperbolic conservation laws. The key idea of the technique is to construct basis functions that are local in parameter and time…
Echo cancellation and noise reduction are essential for full-duplex communication, yet most existing neural networks have high computational costs and are inflexible in tuning model complexity. In this paper, we introduce time-frequency…
Many real-world 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 in the field of computer vision. Recently, the alignment problem…
The efficiency of boundary element methods depends crucially on the time required for setting up the stiffness matrix. The far-field part of the matrix can be approximated by compression schemes like the fast multipole method or…
Multi-resolution methods such as Adaptive Mesh Refinement (AMR) can enhance storage efficiency for HPC applications generating vast volumes of data. However, their applicability is limited and cannot be universally deployed across all…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one and their investigation has experienced several efforts from many researchers in the…
The numerical solution of dynamical systems with memory requires the efficient evaluation of Volterra integral operators in an evolutionary manner. After appropriate discretisation, the basic problem can be represented as a matrix-vector…
This paper develops an interpolatory framework for weighted-$\mathcal{H}_2$ model reduction of MIMO dynamical systems. A new representation of the weighted-$\mathcal{H}_2$ inner products in MIMO settings is introduced and used to derive…
Modern scientific instruments produce vast amounts of data, which can overwhelm the processing ability of computer systems. Lossy compression of data is an intriguing solution, but comes with its own drawbacks, such as potential signal…
This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon…
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…
The design of numerical boundary conditions is a challenging problem that has been tackled in different ways depending on the nature of the problem and the numerical scheme used to solve it. In this paper we present a new weighted…
We propose an iterative solution method for the 3D high-frequency Helmholtz equation that exploits a contour integral formulation of spectral projectors. In this framework, the solution in certain invariant subspaces is approximated by…