Gauss Elimination Method Pseudocode

Earlier in Gauss Elimination Method Algorithm, we discussed about an algorithm for solving systems of linear equation having n unknowns. In this tutorial we are going to develop pseudocode for this method so that it will be easy while implementing using programming language.

Pseudocode for Gauss Elimination Method

1. Start

2. Input the Augmented Coefficients Matrix (A):
	
	For i = 1 to n
		
		For j = 1 to n+1
			
			Read Ai,j
		
		Next j
	
	Next i

3. Apply Gauss Elimination on Matrix A:
	
	For i = 1 to n-1
		
		If Ai,i = 0
			
			Print "Mathematical Error!"
			Stop
		
		End If
		
		For j = i+1 to n
			
			Ratio = Aj,i/Ai,i
			
			For k = 1 to n+1
				
				Aj,k = Aj,k - Ratio * Ai,k
			
			Next k
		Next j
	Next i

4. Obtaining Solution by Back Substitution:
	
	Xn = An,n+1/An,n
	
	For i = n-1 to 1 (Step: -1)
		
		Xi = Ai,n+1
		
		For j = i+1 to n
			
			Xi = Xi - Ai,j * Xj
		
		Next j
		
		Xi = Xi/Ai,i
	Next i

5. Display Solution:
	
	For i = 1 to n
		
		Print Xi
	
	Next i

6. Stop


---------------
Note: All array indexes are assumed to start from 1.

Recommended Readings

1. Gauss Elimination Method Algorithm
2. Gauss Elimination Method Pseudocode
3. Gauss Elimination Method Using C
4. Gauss Elimination Method Using C++