Python Code

Given a unit lower triangular matrix L and an upper triangular matrix U. Write a python code to find LU decomposition.

the lower triangular system Ly = b,

the upper triangular system Ux = y.

The solution with L is referred to as forward elimination, whereas the solution with U is referred to as backward elimination.

The algorithms like that:

Write the forward and backward elimination solves (Ly = b and U x = y).

Text file is the matrix. Read the matrix from given text file. Text file is something like this:

23 3 0.000001370542294

4 4 0.107816040610854

7 4 0.022782277293175

11 4 -0.00921782470662

.. ..

.. ..

.. ..

The file contains 50 lines.

Algorithm 1.1 (Forward elimination). Let L = (lij).j=1 be unit lower triangular, i.e., lii = 1 and lij = 0 for i j. For a given y e R", to find the solution x ERM of Lx = y, we proceed as follows: For i = n, In = Yn; For i = n - 1, n - 2, ..., 1, we compute 1 (yi Wi,i+12i+1 Winkn). Unn 2 i Uji End loop on i. Algorithm 1.1 (Forward elimination). Let L = (lij).j=1 be unit lower triangular, i.e., lii = 1 and lij = 0 for i j. For a given y e R", to find the solution x ERM of Lx = y, we proceed as follows: For i = n, In = Yn; For i = n - 1, n - 2, ..., 1, we compute 1 (yi Wi,i+12i+1 Winkn). Unn 2 i Uji End loop on