Algorithmic Solution for Systems of Linear Equations, in $\mathcal{O}(mn)$ time
Abstract
We present a novel algorithm attaining excessively fast, the sought solution of linear systems of equations. The algorithm is short in its basic formulation and, by definition, vectorized, while the memory allocation demands are trivial, because, for each iteration, only one dimension of the given input matrix is utilized. The execution time is very short compared with state-of-the-art methods, exhibiting speed-up and low memory allocation demands, especially for non-square Systems of Linear Equations, with ratio of equations versus features high (tall systems), or low (wide systems) accordingly. The accuracy is high and straightforwardly controlled, and the numerical results highlight the efficiency of the proposed algorithm, in terms of computation time, solution accuracy and memory demands. The paper also comprises a theoretical proof for the algorithmic convergence, and we extend the implementation of the proposed algorithmic rationale to feature selection tasks.
Cite
@article{arxiv.2104.12570,
title = {Algorithmic Solution for Systems of Linear Equations, in $\mathcal{O}(mn)$ time},
author = {Nikolaos P. Bakas},
journal= {arXiv preprint arXiv:2104.12570},
year = {2023}
}