2025/07/08 by Lamjahdi, Mohamed El Mami
Mathematics · #500 | Naturwissenschaften #Control Theory #FOS: Mathematics #Linear Systems #Mathematics #Matrix #Phyics #Time Complexity
paper · doi:10.15488/19228
For decades, Gaussian and Gauss-Jordan elimination have stood as the standard tools for solving linear systems. These methods, though reliable, come with a price: time. Specifically, they involve computational complexity on the order of O(n3), which becomes a bottleneck in real-time and high-precision applications. This post introduces and formalizes three alternative methods: The 2X Method (for 2×2 systems) A direct constant-time Matrix Inversion The Gitter / 4X Method (for 3×3 systems) These methods provide constant-time performance (O(1)), achieved through visual cross-structure logic, not row manipulation or pivoting. By replacing multi-step algorithms with single-step visual-algebraic identities, they aim to outperform traditional methods both in speed and conceptual clarity.