Gauss-seidel Method

Gauss-Seidel Method:

To understand the GaussSeidel method, we consider a system of 3 linear equations in 3 variables:

These equations may be rewritten as;

Now we start with the initial values y₀, z₀ and compute x₁ from the first equation, i.e.,

while using second equation to compute y₁, we use z₀, x₁ for z and x (we are taking x₀)

Now to compute z, for third equation, we use x₁ and y₁, i.e.,

In gereral, this procedure may written as following recurrence relation;