Manuals/calci/CHOLESKY

CHOLESKY(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   =  
  is lower triangular with positive diagonal elements
  is is the conjugate transpose value of  
  • Every Hermitian positive-definite matrix has a unique Cholesky decomposition.
  • Here  ,   is set of values to find the factorization value.
  • Partition matrices in   =   is

 

Algorithm

  1. Determine   and  

  =     =  

  1. Compute   from

  =   this is a Cholesky Factorization of order  

ZOS Section

Examples

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

Result
4 0 0
3 3 0
-1.25 1.25 2.80624

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

Result
5 0 0
3 3 0
-1 1 3

See Also