Difference between revisions of "Manuals/calci/CHOLESKY"

Revision as of 23:57, 8 April 2015

CHOLESKY(arr)

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  $L$

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

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

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   <math>L</math> is lower triangular with positive diagonal elements
   <math>L^{T}</math> is is the conjugate transpose value of <math>L</math>
-*Every Hermitian positive-definite matrix (and thus also every real-valued symmetric positive-definite matrix) has a unique Cholesky decomposition.
+*Every Hermitian positive-definite matrix  has a unique Cholesky decomposition.
 *Here <math>CHOLESKY(arr)</math>, <math>arr</math> is set of values to find the factorization value.
-*Partition matrices in as <math>A</math> = <math>LL^{T}</math> (Please take the description from http://www.seas.ucla.edu/~vandenbe/103/lectures/chol.pdf )
+*Partition matrices in as <math>A</math> = <math>LL^{T}</math>
 ==ZOS Section==