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Solve Using Gauss Jacobi Iteration Method 2𝒙 + 12y + Z – 4w = 13 13𝒙 + 5y - 3z + W = 18 2𝒙 + Y – 3z + 9w = 31 3𝒙 - 4y + 10z + W = 29 - Applied Mathematics 1

Sum

Solve using Gauss Jacobi Iteration method 
2𝒙 + 12y + z – 4w = 13
13𝒙 + 5y - 3z + w = 18
2𝒙 + y – 3z + 9w = 31
3𝒙 - 4y + 10z + w = 29

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Solution

`x=(18-5y+3z-w)`

`y=(13-2x-z+4w)`

`z=(29-3x+4y-w)`

`w=(31-2x-y+3z)/9`

Iteration x y z w
1 1.3846 1.0833 2.9 3.4444
2 1.3722 1.7590 2.5735 3.9831
3 0.9956 1.9679 2.7936 3.8019
4 0.9800 1.9519 3.0083 3.9357
5 1.0254 1.9812 2.9932 4.0126
6 1.0047 2.0005 2.9836 3.9942
7 0.9965 1.9987 2.9994  
8 1.0009 1.9984 3.0012  
9 1.0008 2.0000 2.9990  
10 0.9997 2.0001 2.9997  
11 0.9999 1.9999 3.0002  
12 1.0001 2 3  
13 1 2 3  

∴ x = 1, y = 2, z = 3, w = 4.

Concept: Gauss Jacobi Iteration Method
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