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A lot of recent progress has been made in ultra low-bit quantization, promising significant improvements in latency, memory footprint and energy consumption on edge devices. Quantization methods such as Learned Step Size Quantization can…
In this paper, a fast multipole method (FMM) is proposed for 3-D Laplace equation in layered media. The potential due to charges embedded in layered media is decomposed into a free space component and four types of reaction field…
A critical factor in adopting machine learning for time-sensitive financial tasks is computational speed, including model training and inference. This paper demonstrates that a broad class of such problems, especially those previously…
An important component of many image alignment methods is the calculation of inner products (correlations) between an image of $n\times n$ pixels and another image translated by some shift and rotated by some angle. For robust alignment of…
In this work we apply commonly known methods of non-adaptive interpolation (nearest pixel, bilinear, B-spline, bicubic, Hermite spline) and sampling (point sampling, supersampling, mip-map pre-filtering, rip-map pre-filtering and FAST) to…
In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained…
Fluorescence Molecular Tomography (FMT) is a widely used non-invasive optical imaging technology in biomedical research. It usually faces significant accuracy challenges in depth reconstruction, and conventional iterative methods struggle…
Kernel methods are extensively employed for nonlinear data clustering, yet their effectiveness heavily relies on selecting suitable kernels and associated parameters, posing challenges in advance determination. In response, Multiple Kernel…
Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation…
This work presents an approach for automating the discretization and approximation procedures in constructing digital representations of composites from Micro-CT images featuring intricate microstructures. The proposed method is guided by…
Kernel based approximation offers versatile tools for high-dimensional approximation, which can especially be leveraged for surrogate modeling. For this purpose, both "knot insertion" and "knot removal" approaches aim at choosing a suitable…
The Kohn-Sham method uses a single model system, and corrects it by a density functional the exact user friendly expression of which is not known and is replaced by an approximated, usable, model. We propose to use instead more than one…
We introduce a Fourier-based fast algorithm for Gaussian process regression in low dimensions. It approximates a translationally-invariant covariance kernel by complex exponentials on an equispaced Cartesian frequency grid of $M$ nodes.…
Extreme Learning Machine (ELM) is an efficient and effective least-square-based learning algorithm for classification, regression problems based on single hidden layer feed-forward neural network (SLFN). It has been shown in the literature…
The Nystr\"om method is a convenient heuristic method to obtain low-rank approximations to kernel matrices in nearly linear complexity. Existing studies typically use the method to approximate positive semidefinite matrices with low or…
Non-negative Matrix Factorization(NMF) algorithm can only be used to find low rank approximation of original non-negative data while Concept Factorization(CF) algorithm extends matrix factorization to single non-linear kernel space,…
Resampling by interpolation is the traditional method to process interferograms from non-uniformly sampled Fourier transform spectrometers. The non-uniform fast Fourier transform (NUFFT) is an alternative approach that has been mostly…
Conventional physics-informed extreme learning machine (PIELM) often faces challenges in solving partial differential equations (PDEs) involving high-frequency and variable-frequency behaviors. To address these challenges, we propose a…
In this paper we develop the first fine-grained rounding error analysis of finite element (FE) cell kernels and assembly. The theory includes mixed-precision implementations and accounts for hardware-acceleration via matrix multiplication…
Recent feature matching methods have achieved remarkable performance but lack efficiency consideration. In this paper, we revisit the mainstream detector-free matching pipeline and improve all its stages considering both accuracy and…