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Difference between Gauss Elimination Method and Gauss Jordan Method | Numerical Method

  • Last Updated : 04 Nov, 2021

Gauss Elimination Method:

Gauss Elimination Method is one of the most widely used methods. This method is a systematic process of eliminating unknowns from the linear equations. This method is divided into two linear equations:

  • Triangularization Method
  • Back Substitution Method

Gauss Jordan Method:

Gauss Jordan Method is a little modification of the Gauss Elimination Method. Here, during the stages of elimination, the coefficients are eliminated in such a way that the systems of equations are reduced to a diagonal matrix. The very first method of the Gauss Jordan Method involves the elimination of the first variable i.e. x from all the equations except the first equation. Then it eliminates the second variable i.e. x2 from all the equations except the second equation and so on proceeding in this manner, finally we eliminate the last variable i.e. in from all the equations except the last equation.

Sr.NoGauss Elimination MethodGauss Jordan Method
1.In this method, the unknowns are eliminated successively and the system is reduced to an upper triangular system from which the unknowns are found by back substitution.    In this method, elimination of unknowns is performed  by all equations not only from equations to follow. Thus the system ultimately reduces to a diagonal matrix form i.e. each equation involving only one unknowns.
2.

Finding the solution of n simultaneous linear equation, the number of multiplications and divisions are of the order. n3/3.



For Example: 

if n=5, the number of multiplications and divisions ISI elimination is approximately 42.

Finding the solution of n simultaneous linear equation, the number of multiplications and divisions are of the order. n3/2.

For Example:

if n=5, the number of multiplications and divisions are approximately 62.

3.It does not seem to be easier but requires about 50 percent fewer operations than Gauss Jordan Method.It seems to be easier but requires about 50 percent fewer operations than Gauss elimination  Method.
4.For large systems, Gauss Elimination Method is not preferred.For large systems, Gauss Jordan Method is preferred to Gauss Elimination Method

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