The matrix P is always positive semi-definite and can be decomposed into LL.
The correlation matrix is decomposed, to give the lower-triangular L.
Applying this to a vector of uncorrelated samples u produces a sample vector Lu with the covariance properties of the system being modeled..
For linear systems that can be put into symmetric form, the Cholesky decomposition (or its LDL variant) is the method of choice, for superior efficiency and numerical stability.
Compared to the LU decomposition, it is roughly twice as efficient.
The Cholesky decomposition is unique when A is positive definite; there is only one lower triangular matrix L with strictly positive diagonal entries such that A = LL*.
However, the decomposition need not be unique when A is positive semidefinite.IET members benefit from discounts to all IET publications and free access to E&T Magazine.If you are an IET member, log in to your account and the discounts will automatically be applied.For these reasons, the LDL decomposition may be preferred.For real matrices, the factorization has the form A = LDL.The Cholesky algorithm, used to calculate the decomposition matrix L, is a modified version of Gaussian elimination.