In this paper, we propose an inexact inverse iteration method for the computation of the eigenvalue with the smallest modulus and its associated eigenvector for a large sparse matrix. The linear systems of the traditional inverse iteration are solved with accuracy that depends on the eigenvalue with the second smallest modulus and iteration numbers. We prove that this approach preserves the linear convergence of inverse iteration. We also propose two practical formulas for the accuracy bound which are used in actual implementation.
|Number of pages||13|
|Journal||Numerical Linear Algebra with Applications|
|State||Published - 1 Jan 1997|
- Inexact inverse iteration
- Large eigenvalue problem
- Linear convergence