Description
Gauss-Seidel Method is an iterative method for solving Linear System Equations with the
unknown variables. It is named after the mathematician Carl Freidrich Gausss (1777-1855) and Philipp L.
Seidel (1821-1896). Gauss- Seidel Method is a modification of Gauss Jacobi Method. Since, it is a
modifiaction, it is not more difficult to solve than Gauss Jacobi becuase, it often requires lesser iterations
to produce the same level of accuracy.
The difference in solving Gauss Jacobi and Gauss-Seidel is the used of initial value in iterating the
rearrange equation wherein, in Gauss Jacobi, the initial value of the unknown variables ( for instance, x1,
x2,x3) must be substitute to zero, then the resulting value will be used in second iteration. While in Gauss
Seidel, the the value of x1 from the first rearranged equation must be determined first so, the initial value
zero (0) will only be substituted to x2 and x3. Once the value of x1 is determined, it will be used in the
second equation to determined the x2. Similary, the value of x1 and x2 will be used to determine the
value of x3 in the third equation.
To wrap up the steps in solving Gauss Seidel, the value of unknown immediately reduces the
number of iterations, the calculated value replace the earlier value only at the end of the iteration.
Because of it, the gauss-seidel methods converges much faster than the Gauss Jacobi method.
Thus, GausS-Seidel Method allows us to control round-off error because it is more accurate than
other iteration methods. Also, it is simple and easy to use especially in computer when computing.