Perform four iterations (rounded to four decimal places) using

Question

Perform four iterations (rounded to four decimal places) using
(i) Jacobi Method and
(ii) Gauss-Seidel method ,
for the following system of equations.

02 Aug 2023

Answer :

Word Count : 621

To solve a system of equations using the Jacobi Method and the Gauss-Seidel Method, we need to perform iterations until we reach a desired level of accuracy or convergence. Let's consider the following system of equations:

Equation 1: 3x + y + z = 5
Equation 2: x + 4y - z = 3
Equation 3: 2x - y + 6z = 2

To apply the Jacobi Method and the Gauss-Seidel Method, we need to rewrite the equations in an iterative form, where each variable is solved for in terms of the other variables. Let's rearrange the equations:

Equation 1: x = (5 - y - z) / 3
Equation 2: y = (3 - x + z) / 4
Equation 3: z = (2 - 2x + y) / 6

Now, we can start the iterations:

(i) Jacobi Method:
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