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Difference between Gauss Jordan Method and Gauss Siedel Method

In this article we will see the differences between Gauss Jordan Method and Gauss Siedel Method.

Difference between Gauss Jordan Method and Gauss Siedel Method

Gauss Jordan 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.

Gauss Siedel Method:

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.

Following are the differences between the Gauss Jordan and Gauss Siedel Method

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.

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