Name
Title | ||
|---|---|---|
SOAR: A Second-order Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem |
Abstract | ||
|---|---|---|
We first introduce a second-order Krylov subspace $\mathcal{G}_n$(A,B;u) based on a pair of square matrices A and B and a vector u. The subspace is spanned by a sequence of vectors defined via a second-order linear homogeneous recurrence relation with coefficient matrices A and B and an initial vector u. It generalizes the well-known Krylov subspace $\mathcal{K}_n$(A;v), which is spanned by a sequence of vectors defined via a first-order linear homogeneous recurrence relation with a single coefficient matrix A and an initial vector v. Then we present a second-order Arnoldi (SOAR) procedure for generating an orthonormal basis of $\mathcal{G}_n$(A,B;u). By applying the standard Rayleigh--Ritz orthogonal projection technique, we derive an SOAR method for solving a large-scale quadratic eigenvalue problem (QEP). This method is applied to the QEP directly. Hence it preserves essential structures and properties of the QEP. Numerical examples demonstrate that the SOAR method outperforms convergence behaviors of the Krylov subspace--based Arnoldi method applied to the linearized QEP. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1137/S0895479803438523 | SIAM J. Matrix Analysis Applications |
Keywords | Field | DocType |
second-order krylov subspace,quadratic eigenvalue problem,linearized qep,initial vector v,soar method,coefficient matrices a,initial vector u,second-order arnoldi method,well-known krylov subspace,second-order arnoldi,krylov subspace,rayleigh-ritz orthogonal projection,second-order arnoldi procedure,arnoldi method,orthogonal projection,first order,second order,recurrence relation | Krylov subspace,Mathematical optimization,Coefficient matrix,Generalized minimal residual method,Recurrence relation,Matrix (mathematics),Square matrix,Orthonormal basis,Quadratic eigenvalue problem,Mathematics | Journal |
Volume | Issue | ISSN |
26 | 3 | 0895-4798 |
Citations | PageRank | References |
45 | 3.07 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhaojun Bai | 1 | 661 | 107.69 |
| Yangfeng Su | 2 | 235 | 22.05 |