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
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.