The Gauss-Seidel method is an iterative technique used to solve systems of linear equations. A computational tool implementing this method typically accepts a set of equations and initial variable guesses, then refines these guesses through repeated calculations until a solution of acceptable accuracy is reached. For example, given equations like 2x + y = 5 and x – 3y = -2, the tool would systematically adjust initial estimates for ‘x’ and ‘y’ until values satisfying both equations are found.
This iterative approach offers advantages in solving large systems of equations, often converging faster than similar methods like Jacobi iteration, especially for diagonally dominant systems. Historically rooted in the work of Carl Friedrich Gauss and Philipp Ludwig von Seidel in the 19th century, this method remains relevant in various scientific and engineering disciplines, from electrical circuit analysis to fluid dynamics simulations, due to its relative computational efficiency and ease of implementation.
