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6. Gauss Jacobi method example ( Enter your problem )
  1. Example `2x+5y=21,x+2y=8`
  2. Example `2x+5y=16,3x+y=11`
  3. Example `x+y+z=3,2x-y-z=3,x-y+z=9`
  4. Example `x+y+z=7,x+2y+2z=13,x+3y+z=13`
Other related methods
  1. Inverse Matrix method
  2. Cramer's Rule method
  3. Gauss-Jordan Elimination method
  4. Gauss Elimination Back Substitution method
  5. Gauss Seidel method
  6. Gauss Jacobi method
  7. Elimination method
  8. LU decomposition using Gauss Elimination method
  9. LU decomposition using Doolittle's method
  10. LU decomposition using Crout's method
  11. Cholesky decomposition method
  12. SOR (Successive over-relaxation) method
  13. Relaxation method

5. Gauss Seidel method
(Previous method)
2. Example `2x+5y=16,3x+y=11`
(Next example)

1. Example `2x+5y=21,x+2y=8`





1. Solve Equations 2x+5y=21,x+2y=8 using Gauss Jacobi method

Solution:
Total Equations are `2`

`2x+5y=21`

`x+2y=8`


From the above equations
`x_(k+1)=1/2(21-5y_(k))`

`y_(k+1)=1/2(8-x_(k))`

Initial gauss `(x,y) = (0,0)`

Solution steps are
`1^(st)` Approximation

`x_1=1/2[21-5(0)]=1/2[21]=10.5`

`y_1=1/2[8-(0)]=1/2[8]=4`

`2^(nd)` Approximation

`x_2=1/2[21-5(4)]=1/2[1]=0.5`

`y_2=1/2[8-(10.5)]=1/2[-2.5]=-1.25`

`3^(rd)` Approximation

`x_3=1/2[21-5(-1.25)]=1/2[27.25]=13.625`

`y_3=1/2[8-(0.5)]=1/2[7.5]=3.75`

`4^(th)` Approximation

`x_4=1/2[21-5(3.75)]=1/2[2.25]=1.125`

`y_4=1/2[8-(13.625)]=1/2[-5.625]=-2.8125`

`5^(th)` Approximation

`x_5=1/2[21-5(-2.8125)]=1/2[35.0625]=17.5312`

`y_5=1/2[8-(1.125)]=1/2[6.875]=3.4375`

`6^(th)` Approximation

`x_6=1/2[21-5(3.4375)]=1/2[3.8125]=1.9062`

`y_6=1/2[8-(17.5312)]=1/2[-9.5312]=-4.7656`

`7^(th)` Approximation

`x_7=1/2[21-5(-4.7656)]=1/2[44.8281]=22.4141`

`y_7=1/2[8-(1.9062)]=1/2[6.0938]=3.0469`


Equations are Divergent...
Intertions are tabulated as below
Iterationxy
110.54
20.5-1.25
313.6253.75
41.125-2.8125
517.53123.4375
61.9062-4.7656
722.41413.0469



This material is intended as a summary. Use your textbook for detail explanation.
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5. Gauss Seidel method
(Previous method)
2. Example `2x+5y=16,3x+y=11`
(Next example)





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