The Gauss-Seidel technique is an iterative method used to resolve programs of linear equations. A computational instrument implementing this technique sometimes accepts a set of equations and preliminary variable guesses, then refines these guesses by repeated calculations till an answer of acceptable accuracy is reached. For instance, given equations like 2x + y = 5 and x – 3y = -2, the instrument would systematically modify preliminary estimates for ‘x’ and ‘y’ till values satisfying each equations are discovered.
This iterative strategy provides benefits in fixing massive programs of equations, typically converging sooner than comparable strategies like Jacobi iteration, particularly for diagonally dominant programs. Traditionally rooted within the work of Carl Friedrich Gauss and Philipp Ludwig von Seidel within the nineteenth century, this technique stays related in numerous scientific and engineering disciplines, from electrical circuit evaluation to fluid dynamics simulations, because of its relative computational effectivity and ease of implementation.
