damieee/ele527groupproject

This code solves a system of linear equations using the Gauss-Seidel method. It takes as input a coefficient matrix, a right-hand side vector, an initial guess for the solution vector, and the number of iteration steps to perform.

Function:

gauss_seidel(A, b, x0, num_of_iteration)

Description:

This function implements the Gauss-Seidel method for solving a system of linear equations.

Parameters:

• A: Coefficient matrix (list of lists)
• b: Right-hand side vector (list)
• x0: Initial guess for the solution vector (list)
• num_of_iteration: Number of iteration steps to perform (integer)

Returns:

• The final solution vector (list)

IMPORTED MODULES

Module:

art

Description: This module provides ASCII art text for the program logo.

USED METHOD

Method:

copy()

Description: This method is used to create a deep copy of the initial guess solution vector 'x0'. It ensures that the original 'x0' remains unchanged during the iterations.

MAIN CODE

• Coefficient matrix:

  • A = [[1, 9, -2], [2, -1, 8], [6, 1, 1]]

• Right-hand side vector:

  • b = [36, 121, 107]

• Initial guess for the solution vector:

  • x0 = [0, 0, 0]

• Number of iteration steps:

  • num_steps = 10

• Solve the system of equations using the Gauss-Seidel method:

  • solution = gauss_seidel(A, b, x0, num_steps)

• Print the program logo:

  • print(logo)

• Print the solution rounded to 6 significant digits:

  • for i, value in enumerate(solution):
    • print(f"x{i + 1} = {value:.6g}")

HOW TO RUN LOCALLY

1. Ensure that you have the required dependencies installed. You can install the necessary packages using pip:

2. Copy the code into a Python file (e.g., linear_equations_solver.py).

3. Run the Python script:

The solution for the system of linear equations will be displayed in the console output.