Abstract
We give two generalizations of the induced dimension reduction (IDR) approach for the solution of linear
systems. We derive a flexible and a multi-shift quasi-minimal residual IDR variant. These variants are based
on a generalized Hessenberg decomposition. We present a new, more stable way to compute basis vectors
in IDR. Numerical examples are presented to show the effectiveness of these new IDR variants and the new
basis compared with existing ones and to other Krylov subspace methods.
systems. We derive a flexible and a multi-shift quasi-minimal residual IDR variant. These variants are based
on a generalized Hessenberg decomposition. We present a new, more stable way to compute basis vectors
in IDR. Numerical examples are presented to show the effectiveness of these new IDR variants and the new
basis compared with existing ones and to other Krylov subspace methods.
| Original language | English |
|---|---|
| Pages (from-to) | 1-25 |
| Number of pages | 25 |
| Journal | Numerical Linear Algebra with Applications |
| Volume | 22 |
| Issue number | 1 |
| Early online date | 1 May 2014 |
| DOIs | |
| Publication status | Published - Jan 2015 |
Keywords
- iterative methods
- IDR
- IDR(s)
- quasi-minimal residual
- Krylov subspace methods
- large sparse nonsymmetric systems