Manuals/calci/CHOLESKY

CHOLESKY(arr)

• $arr$ 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 $CHOLESKY(arr)$, $arr$ 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 )

Examples

CHOLESKY([[16,32,12],[12, 18, 0],[ -5, 0, 11]])

Result

4	0	0
3	3	0
-1.25	1.25	2.80624

CHOLESKY([[25, 15, -5],[15, 18, 0],[ -5, 0, 11]])

Result

5	0	0
3	3	0
-1	1	3