List of magic codes
LU Factorization
LU Factorization is to factorize a square or rectangular matrix 
into an upper-triangular matrix 
and a lower-triangular 
. It can be
applied to the Gaussian Elimination. Also, partial pivoting is used
to handle general cases and reduce the computational errors.
Conjugate Gradient Method for Solving Linear Systems
Conjugate gradient method can be applied to solve linear systems. It requires
the matrix to be positive definite. CG is an iterative method and only
needs the user to provide the matrix-vector operator. In other words, the
explicit form of isn't needed here.