%0 Journal Article
%J SIAM Journal on Matrix Analysis and Applications
%D 2009
%T On the Semidefinite B-Arnoldi Method
%A Stewart, G.W.
%K Arnoldi's method
%K B-inner product
%K null-space component
%K semidefinite B
%X 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 “orthogonalization” 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.
%B SIAM Journal on Matrix Analysis and Applications
%V 31
%P 1458 - 1468
%8 2009///
%G eng
%U http://link.aip.org/link/?SML/31/1458/1
%N 3
%R 10.1137/090759252