Name
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. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1137/090759252 | SIAM J. Matrix Analysis Applications |
Keywords | Field | DocType |
inner product,semi-inner product,generalized eigenvalue problem,positive definite matrix,lambda bx,ordinary arnoldi method,null space,semidefinite b-arnoldi method,b-arnoldi method | Kernel (linear algebra),Applied mathematics,Linear algebra,Vector space,Mathematical analysis,Positive-definite matrix,Algorithm,Eigendecomposition of a matrix,Numerical analysis,Orthogonalization,Mathematics,Lambda | Journal |
Volume | Issue | ISSN |
31 | 3 | 0895-4798 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| G. W. Stewart | 1 | 62 | 8.15 |