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The Barnes-Hut and Fast Multipole Methods are widely utilised methods applied in order to reduce the computational cost of evaluating long range forces in $N$-body simulations. Despite this, applying existing libraries to simple problems…

Boundary element methods produce dense linear systems that can be accelerated via multipole expansions. Solved with Krylov methods, this implies computing the matrix-vector products within each iteration with some error, at an accuracy…

In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…

In this paper, we propose an optimization selection methodology for the ubiquitous sparse matrix-vector multiplication (SpMV) kernel. We propose two models that attempt to identify the major performance bottleneck of the kernel for every…

In this paper, we consider the problem of preamble design in multiple-input multiple-output (MIMO) systems employing offset quadrature amplitude modulation based filter bank multicarrier (OQAM/FBMC) and propose a preamble optimization…

Large Multimodal Models (LMMs) struggle to adapt varying computational budgets due to numerous visual tokens. Previous methods attempted to reduce the number of visual tokens before or within LLMs. However, these strategies inevitably…

This paper proposes a novel scheme for cell-free massive multiple-input multiple-output (CFmMIMO) networks to support any federated learning (FL) framework. This scheme allows each instead of all the iterations of the FL framework to happen…

Accurate interpolation of functions and derivatives is crucial in solving partial differential equations (PDEs). The Radial Basis Function (RBF) method has become an extremely popular and robust approach for interpolation on scattered data.…

In many practical applications of numerical methods a substantial increase in efficiency can be obtained by using local grid refinement, since the solution is generally smooth in large parts of the domain and large gradients occur only…

In this paper, we propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex…

We propose a novel Krylov subspace method for estimating the finite impulse response (FIR) of a one-dimensional linear time-invariant systems. The method approximates the system's FIR using a kernel-based formulation combined with…

In this study, a fast multipole method (FMM) is used to decrease the computational time of a fully-coupled poroelastic hydraulic fracture model with a controllable effect on its accuracy. The hydraulic fracture model is based on the…

We develop a general equality-constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970). Although it was historically considered to be computationally prohibitive in practice, we demonstrate…

Many kernel methods suffer from high time and space complexities and are thus prohibitive in big-data applications. To tackle the computational challenge, the Nystr\"om method has been extensively used to reduce time and space complexities…

Based upon the fast computation of the coefficients of the interpolation polynomials at Chebyshev-type points by FFT, DCT and IDST, respectively, together with the efficient evaluation of the modified moments by forwards recursions or by…

We investigate a range of techniques for the acceleration of Calder\'on (operator) preconditioning in the context of boundary integral equation methods for electromagnetic transmission problems. Our objective is to mitigate as far as…

Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…

Large language models (LLMs) have transformed the way we think about language understanding and generation, enthralling both researchers and developers. However, deploying LLMs for inference has been a significant challenge due to their…

Boundary integral equation methods are widely used in the solution of many partial differential equations. The kernels that appear in these surface integrals are nearly singular when evaluated near the boundary, and straightforward…

In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…