Mastering Python for Finance - Second Edition

The Gauss-Seidel method

The Gauss-Seidel method works very much like the Jacobi method. It is another way to solve a square system of linear equations using an iterative procedure with the equation in the form of Ax=B. Here, the A matrix is decomposed as A=L+U, where the A matrix is a sum of a lower triangular matrix, L, and an upper triangular matrix, U. Let's take a look at the example of a 4 x 4 A matrix:

The solution is then obtained iteratively, as follows:

Using a lower triangular matrix, L, where zeroes fill up the upper triangle, ...