Use the described general schema to build your own method

Question

In Homework, you have solved the following linear system using the Jacobi and Gauss-Seidel methods:

5x₁ - 2x₂ + 3x_n = -1

-3x₁ + 9X₂ + x_n = 2

2x₁ - x₂ - 7x_n = 3

The details of both methods are included below for reference.

Both methods, Jacobi and Gauss-Seidel, were developed using the general schema for iteration methods. The logic is based on selecting the matrices N and P, for both methods.

Using the same logic, use the described general schema to build your own method for solving the given linear system. Implement your algorithm and then compare results with the Jacobi and Gauss-Seidel techniques (you already have the algorithms from HW2).

Comment on convergence speed and accuracy and discuss the reasons that make your technique better or worse than the Jacobi and Gauss-Seidel methods.