Gaussian Elimination Matlab Code and Applications

What is Gaussian Elimination (Also known as row reduction process): Gaussian Elimination is a technique of row reduction method in a linear equation. For the reduction number of rows in the linear equation, the equation needs to be transformed in matrix format. This type of numerical analysis algorithm was first used by Carl Friedrich Gauss in 1810. 

Application of Gaussian Elimination:

1. This algorithm is used for solving a linear equation.
2. To solve linear equations or mesh-connected processors.
3. To minimize a linear equation.
4. Fingerprint Image Improvement through a gaussian filtering process in the image processing system.
5. To solve a scheduling algorithm in Operating System.

Gaussian Elimination Matlab Code:

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Mat_Left_side = [25 5 1

64 8 1

144 12 1]

Mat_Left_side = 3×3

25 5 1
64 8 1
144 12 1

Mat_Right_side=[106.8;177.2;279.2]

Mat_Right_side = 3×1

106.80
177.20
279.20

Merge_Mat = [Mat_Left_side Mat_Right_side];

[row,column] = size(Merge_Mat);

%Part 1: Forward elemination

for j=1:row

for i = j+1:row

Merge_Mat(i,:) = Merge_Mat(i,:) - (Merge_Mat(i,j).*Merge_Mat(j,:))./Merge_Mat(j,j) ;

end

end

Merge_Mat

Merge_Mat = 3×4

25.0 5.0 1.0 106.80
0 -4.800 -1.56 -96.2080
0 0 0.7 0.7600

Merge_Mat(1:3,1:3) %The Final Forward elimination matrix

ans = 3×3

25.00 5.0 1.0
0 -4.8 -1.56
0 0 0.70

%Part 2: Back substitution

Final_Right_side_Mat = Merge_Mat(row,column)/Merge_Mat(row,row);

for i = row:-1:2

mat = Merge_Mat(i-1,i:row);

Final_value = (Merge_Mat(i-1,column)-(mat*Final_Right_side_Mat))/(Merge_Mat(i-1,i-1));

Final_Right_side_Mat = [Final_value;Final_Right_side_Mat];

end

Final_value

Final_value = 0.2905

Final_Right_side_Mat %The Final Back substitution matrix

Final_Right_side_Mat = 3×1

0.2905
19.6905
1.0857