Build a Desktop and Android-Based Gauss-Seidel Method SPL Calculator - Febry Wulandari; Nazwa Endhita Hariyanto; Nadya Husenti (Lembaga Penelitian dan Pengabdian Masyarakat Methodist Binjai, 2026)
Systems of Linear Equations (SLE) play a critical role across multiple disciplines including engineering, physics, and quantitative economics. Manual resolution is error-prone, especially as system dimensionality increases. This research presents the design and development of a digital calculator implementing the Gauss-Seidel iterative method to solve m×n SLE automatically, on both Java Swing desktop and React Native Android platforms. Three solution scenarios are supported: square systems (m=n) via direct Gauss-Seidel iteration, overdetermined systems (m>n) via normal least-squares equations, and underdetermined systems (m<n) via minimum-norm solutions. Key features include convergence graph visualization, step-by-step iteration navigation, diagonal dominance analysis, and full iteration history. Testing on 3×3 to 4×4 systems yields RMSE below 10⁻⁶ with convergence within 20 iterations for diagonally dominant matrices, confirming the effectiveness of a multiplatform approach for numerical software in educational and professional contexts.