@article {17725,
	title = {On the Semidefinite B-Arnoldi Method},
	journal = {SIAM Journal on Matrix Analysis and Applications},
	volume = {31},
	year = {2009},
	month = {2009///},
	pages = {1458 - 1468},
	abstract = {The B-Arnoldi method is a variant of the ordinary Arnoldi method in which orthogonalization is done with respect to the inner product generated by a positive definite matrix $B$. It arises in connection with the generalized eigenvalue problem $Ax = \lambda Bx$. When $B$ is semidefinite, the algorithm can proceed formally, with {\textquotedblleft}orthogonalization{\textquotedblright} taking place in the semi-inner product generated by $B$. However, it has been observed that components of the Arnoldi vectors lying in the null space of $B$ can grow rapidly. In this paper we examine the source and consequences of this growth.},
	keywords = {Arnoldi{\textquoteright}s method, B-inner product, null-space component, semidefinite B},
	doi = {10.1137/090759252},
	url = {http://link.aip.org/link/?SML/31/1458/1},
	author = {Stewart, G.W.}
}
