Computer Realization of Solving Tri-diagonal Equations by Gauss-Seidel Method

Gauss - Seidel method is commonly used in solving general linear equations, and there are several known results about the convergence of it. In this paper, the necessary and sufficient conditions of the convergence are presented, which are needed and useful in solving general Tri-diagonal equations by using Gauss - Seidel method. Then the computer algorithm of solving general Tri-diagonal equations is given on the condition of convergence, and this algorithm can efficiently reduce computational time and space complexity. Finally, a numerical example of Tri-diagonal equations solved by Gauss - Seidel method is shown.