ABSTRACT: The nearly analytic discretization of the frequency-domain wave equation produces large-scale, sparse, and ill-conditioned linear system, which challenge conventional iterative solvers. To ...

Abstract: This letter proposes a quaternion projection gradient ascent (QPGA) iterative algorithm based on generalized $\mathbb {HR}$ calculus for computing the principal eigenvalues and its ...

Every day, researchers search for optimal solutions. They might want to figure out where to build a major airline hub. Or to determine how to maximize return while minimizing risk in an investment ...

% This Matlab code solves three-variable non-linear equation f(x) = 0 using Newton-Raphson iterative method [1]. % Ref. [1] S. Chapra, "Applied numerical methods with MATLAB", Mc Craw Hill, Singapore ...

The enormous computing resources needed to train neural networks for artificial intelligence (AI) result in massive power consumption. Researchers have developed a method that is 100 times faster and ...

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where ...

Abstract: Recently, studies have shown the potential of integrating field-type iterative methods with deep learning (DL) techniques in solving inverse scattering problems (ISPs). In this article, we ...

Neural networks are widely adopted in various fields due to their ability to model complex patterns and relationships. However, they face a critical vulnerability to adversarial attacks – small, ...

This repository contains a Python implementation of the Gauss-Seidel Elimination method for solving systems of linear equations. The code reads coefficients from an Excel file (`data.xls`), performs ...