In this article we will see the differences between Gauss Jordan Method and Gauss Siedel Method.
Gauss Jordan Method is a little modification of Gauss Elimination Method. In this method, unknown elements are eliminated from all other equations and not only from the equations to follow. This method is a type of direct method to reduce the matrix to diagonal form by elimination.
This method is superior to Gauss-Jordan Method. The Gauss-Seidel method is an iterative technique that starts with a guess for [x] and improves it with each iteration. The matrix [A] must be diagonally dominant or a solution may not be obtained. It is sometimes called Jacobi iteration.
Sr.No |
Gauss Jordan Method |
Gauss Siedel Method |
1. |
It is a type of a direct method. |
It is a type of iterative methods |
2. |
It uses the process of elimination of the variables from all other rows both below and above the pivotal equation. In this way. this method removes all the off-diagonal terms and thereby produces a diagonal matrix from which we can find out the value of the variables directly. |
In this method, the values of the difference's variables are calculated through successive iterations starting with their initial values at zero. |
3 |
This method is slow for large system |
This method is fast as compared to the Jordan. |
4. |
This method yields a solution of simultaneous linear equations in finite number of steps for any non-singular set of equations. |
In this method, the amount of computation depends on accuracy desired. |
5. |
It is preferable for small systems. |
It is preferable for large systems. |
6. |
This method requires approximately n3^/2 operations which is large number. |
This method requires approximately 2n^2 operations per iteration. |
7. |
It suffers from rounding off errors |
In this method, it has small rounding off errors. |
8. |
This method may always convergent. |
This method may not always convergent, but convergence is guaranteed only under certain circumstances only. When it converges it is superior to the gauss Jordan. |
9. |
This method is preferred when coefficient matrix is sparse i.e. has many zeros. |
This method is preferred over gauss Jordan when coefficient matrix is sparse i.e. has many zeros. |
10. |
In this method, the ill conditioned system can be successfully handled. |
In this method, the ill-conditioned system cannot be successfully handled. |