BibTeX
@ARTICLE{
         Smith1995Dot,
       abstract = "One way to estimate variance components is by restricted maximum likelihood. The
         log-likelihood function is fully defined by the Cholesky factor of a matrix that is usually large
         and sparse. In this article forward and backward differentiation methods are developed for
         calculating the first and second derivatives of the Cholesky factor and its functions. These
         differentiation methods are general and can be applied to either a full or a sparse matrix.
         Moreover, these methods can be used to calculate the derivatives that are needed for restricted
         maximum likelihood, resulting in substantial savings in computation.",
       url = "http://www.jstor.org/stable/1390762",
       author = "S. P. Smith",
       title = "Differentiation of the {C}holesky Algorithm",
       journal = "Journal of Computational and Graphical Statistics",
       volume = "4",
       number = "2",
       year = "1995",
       pages = "134--147",
       ad_theotech = "Hierarchical Approach"
}