# LU decomposition

A factorization of a matrix $LaTeX: A$ into a lower triangular matrix $LaTeX: (L)$ and an upper triangular matrix $LaTeX: (U)$ so that $LaTeX: A=LU$. The advantage is to solve the system $LaTeX: Ax=b$, we first apply forward substitution to solve $LaTeX: Ly=b$, then backward substitution to solve $LaTeX: Ux=y$.