Crout Method

Crout Method: In this method , the coefficient matrix A is decomposed into matrices L and U. Here the matrix L is lower triangular matrix and U is the unit upper triangular matrix.

Let us consider the system of linear equations:

compare these equation with matrix equation AX = B

Suppose we decomposed A = LU such that

Since AX = B and LUX = B implies LY = b, where UX = Y

We have,

       A = LU

Equating coefficients and then on simplification, we get

Now, we have all the values of L and U. Again, We have

      LY = B

With the knowledge of Y, L, U and UX = Y, we can easily compute X. This procedure is called Crout’s Method.