Incomplete Cholesky Factorization

From CFD-Wiki

Cholesky Factorization

When the square matrix A is symmetric and positive definite then it has an efficient triangular decomposition. Symmetric means that a_ij = a_ji for i,j = 1, ... , N. While positive definite means that

In cholesky factorization we construct a lower triangular matrix L whose transpose L^T can itself serve as upper triangular part.
In other words we have
L L^T = A