高斯消元法与高斯乔丹法的区别数值方法

高斯消除法：

高斯消元法是应用最广泛的方法之一。该方法是从线性方程中消除未知数的系统过程。该方法分为两个线性方程：

• 三角化法
• 反向替换法

高斯乔丹法：

Gauss Jordan 方法是 Gauss Elimination Method 的一个小修改。在这里，在消除阶段，系数以这样一种方式消除，即方程组被简化为对角矩阵。 Gauss Jordan 方法的第一个方法涉及从除第一个方程之外的所有方程中消除第一个变量，即 x。然后它从除第二个方程之外的所有方程中消除第二个变量即x2，依此类推，最后我们从除最后一个方程之外的所有方程中消除最后一个变量即in。

Sr.No	Gauss Elimination Method	Gauss 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