Manuals/calci/CHOLESKY

CHOLESKY(ar1)

• $a$ is the array of numeric elements

Description

• This function gives the value of Cholesky factorization.
• It is called cholesky decomposition or cholesky factorization.
• The Cholesky factorization is only defined for symmetric or Hermitian positive definite matrices.Every positive definite matrix A can be factored as $A$ = $LL^{T}$

where

$L$ is lower triangular with positive diagonal elements
$L^{T}$ is is the conjugate transpose value of $L$

• Every Hermitian positive-definite matrix (and thus also every real-valued symmetric positive-definite matrix) has a unique Cholesky decomposition.
• Here $CHOLESKY(array)$,array is set of values to find the factorization value.

Partition matrices in as A= LL^T (Please take the description from http://www.seas.ucla.edu/~vandenbe/103/lectures/chol.pdf )