1 Cholesky Decomposition
A symmetric and positive definite matrix can be efficiently decomposed into a lower and upper triangular matrix. For a matrix of any type, this is achieved by the LU decomposition which factorizes . If satisfies the above criteria, one can decompose more efficiently into where is a lower triangular matrix with positive diagonal elements. is called the Cholesky triangle.
To solve , one solves first for , and then for .
A variant of the Cholesky decomposition is the form , where is upper triangular.
To derive , we simply equate coefficients on both sides of the equation:
Solving for the unknowns (the nonzero s), for and , we get:
- 1 Originally from The Data Analysis Briefbook (http://rkb.home.cern.ch/rkb/titleA.htmlhttp://rkb.home.cern.ch/rkb/titleA.html)
|Date of creation||2013-03-22 12:07:38|
|Last modified on||2013-03-22 12:07:38|
|Last modified by||gufotta (12050)|
|Synonym||matrix square root|