2021/04/26 by Nikolaos Bakas, Bakas, Nikolaos P.
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Computer and information sciences #Machine Learning (cs.LG) #Matrix Theory and Algorithms #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.2104.12570
openalex publication_date 2021/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \mathbf X is utilized. The execution time is very short compared with state-of-the-art methods, exhibiting > × 102 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.