LU Decomposition is an algorithm to decompose a matrix into the from where is the lower triangular matrix and is the upper triangular matrix.
This can be done in MATLAB using the lu function:
lu
[L,U]=lu([4 -2 1;-2 4 -2;1 -2 4]) Copy
[L,U]=lu([4 -2 1;-2 4 -2;1 -2 4])
LU Factorization on Wikipedia and ME 2004 Class Notes.