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  
  2.   =     =  
  3. Compute   from
  4.   =  
  • 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