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 TitleyPeloquin, 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 = "110126",
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"
}
