Gauss-Jacobi’s Method
1) Assuming that the system is diagonally dominant we begin it at rewriting the system in the form
X1 = (C1 – A12X2 – A13X3 …….. A1nXn)/A11
X2 = (C2 – A21X1 – A22X3 …….. A2nXn)/A22
Xn = (Cn – An1X1 – An2X2 …….. A2n n-1Xn-1)/Ann
2) Choose an initial approximation to he solution
k = 0
Let X1 = X2 = Xn = 0
3) Substitute the values of the variables calculated in the previous iteration into the right side of the equation obtained in step 1 to get a new appriximations.
4) Repeat the step 3 until the desired number of iteration is reached and equal values of the unknown are approximately repeatedly.
X1 = (C1 – A12X2 – A13X3 …….. A1nXn)/A11
X2 = (C2 – A21X1 – A22X3 …….. A2nXn)/A22
Xn = (Cn – An1X1 – An2X2 …….. A2n n-1Xn-1)/Ann
2) Choose an initial approximation to he solution
k = 0
Let X1 = X2 = Xn = 0
3) Substitute the values of the variables calculated in the previous iteration into the right side of the equation obtained in step 1 to get a new appriximations.
4) Repeat the step 3 until the desired number of iteration is reached and equal values of the unknown are approximately repeatedly.