LU decomposition

This program obtains the LU decomposition of a matrix using Crout’s Method

Description

This program will obtain the LU decomposition for any square matrix. The LU decomposition method consists of finding the L and U matrices that will satisfy the equation A=L*U, A being a square matrix.

Once L and U found, in order to solve for x, we can rewrite the equation A*x=B as L*x_star=b (Eq.1) where x_star=U*x (Eq.2).

Then we can find x_start by using forward substitution on Equation 1 and finally solve for x using backward substitution on Equation 2.

• MATLAB release: MATLAB 7.9 (2009b)

[Stefan]

Some comments:

- insufficient H1 line

These lines:

check=int8 (L*U)

if check==A
    disp(sprintf (' the equation L*U=A is correct '))
else
    disp(sprintf ('error'))
end

will almost always state an error, because of the casting. Why did you do it that way?

With this sample data:

A=[0 2;3 4];
B=[5;6];

your function gives:

x_soln =

   NaN
   NaN

There is just no pivoting. You didn't limit the usage to strictly regular matrices A. No error check supplied.

Regards,
Stefan