# On the Semidefinite B-Arnoldi Method

 Title On the Semidefinite B-Arnoldi Method Publication Type Journal Articles Year of Publication 2009 Authors Stewart G.W Journal SIAM Journal on Matrix Analysis and Applications Volume 31 Issue 3 Pagination 1458 - 1468 Date Published 2009/// Keywords Arnoldi's method, B-inner product, null-space component, semidefinite B 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 “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. URL http://link.aip.org/link/?SML/31/1458/1 DOI 10.1137/090759252