Difference between revisions of "Manuals/calci/CHOLESKY"
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<math>A_{22}-L_{21}L_{21}^{T}</math> = <math>L_{22}L_{22}^{T}</math> | <math>A_{22}-L_{21}L_{21}^{T}</math> = <math>L_{22}L_{22}^{T}</math> | ||
*this is a Cholesky Factorization of order <math>n-1</math> | *this is a Cholesky Factorization of order <math>n-1</math> | ||
− | <ol> | + | </ol> |
==ZOS Section== | ==ZOS Section== |
Revision as of 07:41, 10 April 2015
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
- Determine and = =
- Compute from =
- this is a Cholesky Factorization of order
ZOS Section
Examples
1. =CHOLESKY([[16,32,12],[12, 18, 0],[ -5, 0, 11]])
4 | 0 | 0 |
3 | 3 | 0 |
-1.25 | 1.25 | 2.80624 |
2. =CHOLESKY([[25, 15, -5],[15, 18, 0],[ -5, 0, 11]])
5 | 0 | 0 |
3 | 3 | 0 |
-1 | 1 | 3 |