University of Guilan Computational Sciences and Engineering 2783-2503 4 2 2025 12 05 Monte Carlo simulation in acceleration Kaczmarz method by the Johnson–Lindenstrauss lemma 331 349 9110 10.22124/cse.2025.31590.1119 EN Somayeh Aghaei Khomami Rasht Municipality Journal Article 2025 08 04 In this paper, we propose an accelerated variant of the randomized Kaczmarz method for solving large-scale linear systems, including both standard and inequality-constrained systems. The key innovation lies in integrating the Johnson–Lindenstrauss (JL) lemma into the row-selection process, which allows high-dimensional rows to be projected onto lower-dimensional spaces while approximately preserving pairwise distances. This enables near-optimal row selection with reduced computational cost, improving both convergence rate and stability, particularly for ill-conditioned systems. Furthermore, Monte Carlo techniques are employed to efficiently construct the projection matrices, enhancing the overall computational performance. Numerical experiments demonstrate that the proposed method achieves faster convergence and higher accuracy compared to traditional randomized Kaczmarz and other conventional techniques, making it highly suitable for large-scale problems in applied mathematics and engineering. https://cse.guilan.ac.ir/article_9110_71727176d5e5cafe414a8f241347260d.pdf