### Abstract

Original language | English |
---|---|

Pages (from-to) | 40-67 |

Number of pages | 28 |

Journal | Electronic Transactions on Numerical Analysis |

Volume | 28 |

Publication status | Published - 2007 |

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### Keywords

- Nonsymmetric generalised eigenproblem
- Inexact inverse iteration

### Cite this

**Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem.** / Freitag, MA; Spence, A.

Research output: Contribution to journal › Article

*Electronic Transactions on Numerical Analysis*, vol. 28, pp. 40-67.

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TY - JOUR

T1 - Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem

AU - Freitag, MA

AU - Spence, A

PY - 2007

Y1 - 2007

N2 - In this paper we consider the computation of a finite eigenvalue and corresponding right eigenvector of a large sparse generalised eigenproblem Ax = Mx using inexact inverse iteration. Our convergence theory is quite general and requires few assumptions on A and M. In particular, there is no need for M to be symmetric positive definite or even nonsingular. The theory includes both fixed and variable shift strategies, and the bounds obtained are improvements on those currently in the literature. In addition, the analysis developed here is used to provide a convergence theory for a verson of inexact simplified Jacobi-Davidson. Several numerical examples are presented to illustrate the theory: including applications in nuclear reactor stability, with M singular and nonsymmetric, the linearised Navier-Stokes equations and the bounded finline dielectric waveguide

AB - In this paper we consider the computation of a finite eigenvalue and corresponding right eigenvector of a large sparse generalised eigenproblem Ax = Mx using inexact inverse iteration. Our convergence theory is quite general and requires few assumptions on A and M. In particular, there is no need for M to be symmetric positive definite or even nonsingular. The theory includes both fixed and variable shift strategies, and the bounds obtained are improvements on those currently in the literature. In addition, the analysis developed here is used to provide a convergence theory for a verson of inexact simplified Jacobi-Davidson. Several numerical examples are presented to illustrate the theory: including applications in nuclear reactor stability, with M singular and nonsymmetric, the linearised Navier-Stokes equations and the bounded finline dielectric waveguide

KW - Nonsymmetric generalised eigenproblem

KW - Inexact inverse iteration

UR - http://etna.mcs.kent.edu/volumes/2001-2010/vol28/abstract.php?vol=28&pages=40-64

UR - http://etna.mcs.kent.edu/volumes/2001-2010/vol28/abstract.php?vol=28&pages=40-64

UR - http://etna.mcs.kent.edu/vol.28.2007/index.html

M3 - Article

VL - 28

SP - 40

EP - 67

JO - Electronic Transactions on Numerical Analysis

JF - Electronic Transactions on Numerical Analysis

SN - 1068-9613

ER -