maths.numerical_analysis.gauss_seidel_method
============================================

.. py:module:: maths.numerical_analysis.gauss_seidel_method


Functions
---------

.. autoapisummary::

   maths.numerical_analysis.gauss_seidel_method.gauss_seidel


Module Contents
---------------

.. py:function:: gauss_seidel(coefficients: list[list[float]], rhs: list[float], tol: float = 1e-10, max_iter: int = 1000) -> list[float]

   Solve the linear system Ax = b using the Gauss-Seidel iterative method.

   Args:
       coefficients (list[list[float]]): Coefficient matrix (n x n)
       rhs (list[float]): Right-hand side vector (n)
       tol (float): Convergence tolerance
       max_iter (int): Maximum number of iterations

   Returns:
       list[float]: Approximate solution vector

   Example:
       >>> A = [[4, 1, 2], [3, 5, 1], [1, 1, 3]]
       >>> b = [4, 7, 3]
       >>> gauss_seidel(A, b)
       [0.5, 1.0, 0.5]

   Wikipedia:
   https://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method