Thomas Method

This method emerges as a simplification of an LU factorization of a tridiagonal matrix.

Saying that A = LU and applying Doolittle where Lii = 1 for i = 1 to n, we get:

Based on the matrix product shown above gives the following expressions:

As far as making the sweep from k = 2 to n leads to the following:

If LUx=r  and Ux=d so Ld=r, then:

After a progressive sustitution we have :

Solving Ux=d afron the regressive sustitution: