BibTeX
@ARTICLE{
         Gratton2014DtM,
       abstract = "The method of conjugate gradients (CG) is widely used for the iterative solution of
         large sparse systems of equations $Ax=b$, where $A\in\Re^{n\times n}$ is symmetric
         positive definite. Let $x_k$ denote the $k$th iterate of CG. This is a nonlinear differentiable
         function of $b$. In this paper we obtain expressions for $J_k$, the Jacobian matrix of $x_k$ with
         respect to $b$. We use these expressions to obtain bounds on $\|J_k\|_2$, the spectral
         norm condition number of $x_k$, and discuss algorithms to compute or estimate $J_kv$ and $J_k^Tv$
         for a given vector $v$.",
       author = "Gratton, S. and Titley-Peloquin, D. and Toint, P. and Ilunga, J.",
       title = "Differentiating the Method of Conjugate Gradients",
       journal = "SIAM Journal on Matrix Analysis and Applications",
       volume = "35",
       number = "1",
       pages = "110--126",
       year = "2014",
       doi = "10.1137/120889848",
       url = "http://dx.doi.org/10.1137/120889848",
       eprint = "http://dx.doi.org/10.1137/120889848",
       ad_area = "Perturbation Analysis"
}