Gauss-Seidel with SOR application

Question

Solving a set of three simultaneous equations using Gauss-Seidel with SOR application in Microsoft Excel. I am aware of the basic procedure. But here is my question:

As I know, in SOR we have to rearrange the equations such that the diagonal coefficient is largest in any equation. However, what if this requirement cant be met? Here is my set of equations, please try helping me which arrangment will fulfil this condition:

(1) 5x 282y 16994z = 1176

(2) 282x 16994y 1081890y = 74579

(3) 16994x 108189y 71949458z = 4945383

How about this order: (3), (2) and (1)

I am not sure if this order is correct! Do help me with this! Thankyou!!!!

Answer 1

I am not sure if I understand your question. Do you just need the values of x, y, z or what?

From the coefficients of x, y, z you've provided

x =  7.940

y = 0.000396

z =  0.0668

Are you trying to use the Jacobi method? There are two types of Gauss-Seidel methods that I am aware of. Gauss-Seidel Iteration method and Gauss-Seidel Elimination method.