Related papers: Efficiently computing the Uhlmann fidelity for den…
Imaging Mueller polarimetry has already proved its potential for metrology, remote sensing and biomedicine. The real-time applications of this modality require both video rate image acquisition and fast data post-processing algorithms.…
Despite their tremendous success and versatility, Deep Neural Networks (DNNs) such as Large Language Models (LLMs) suffer from inference inefficiency and rely on advanced computational infrastructure. To address these challenges and make…
Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
In the recent paper [17] the first experimental determination of the density matrix of a free electron beam has been reported. The employed method leads to a linear inverse problem with a positive semidefinite operator as unknown. The…
Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal…
The Hellmann-Feynman (HF) theorem provides a way to compute forces directly from the electron density, enabling efficient force calculations for large systems through machine learning (ML) models for the electron density. The main issue…
This paper contributes improvements on both the effectiveness and efficiency of Matrix Factorization (MF) methods for implicit feedback. We highlight two critical issues of existing works. First, due to the large space of unobserved…
A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind…
We study a dynamic version of the implicit trace estimation problem. Given access to an oracle for computing matrix-vector multiplications with a dynamically changing matrix A, our goal is to maintain an accurate approximation to A's trace…
Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few…
Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…
We describe an efficient FPGA implementation for the exponentiation of large matrices. The research is related to an algorithm for constructing uniformly distributed linear recurring sequences. The design utilizes the special properties of…
Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distribution, and Monte Carlo sampling…
In this short paper, the authors report a new computational approach in the context of Density Functional Theory (DFT). It is shown how it is possible to speed up the self-consistent cycle (iteration) characterizing one of the most…
In this work we show a rational approximation of the Dawson's integral that can be implemented for high-accuracy computation of the complex error function in a rapid algorithm. Specifically, this approach provides accuracy exceeding $\sim…
Frequency Estimation of a complex exponential is a problem relevant to a large number of fields. In this paper a computationally efficient and accurate frequency estimator is presented using the guaranteed stable Sliding DFT which gives…
In this paper a new fast algorithm for the computation of the distance of a matrix to a nearby defective matrix is presented. The problem is formulated following Alam & Bora (Linear Algebra Appl., 396 (2005), pp.~273--301) and reduces to…
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an…
The Feynman integral is one of the most accurate methods for calculating density operator dynamics in open quantum systems. However, the number of time steps that can realistically be used is always limited, therefore one often obtains an…