Volume 55, pp. 532-546, 2022.
A note on augmented unprojected Krylov subspace methods
Kirk M. Soodhalter
Abstract
Subspace recycling iterative methods and other subspace augmentation schemes are a successful extension to Krylov subspace methods in which
a Krylov subspace is augmented with a fixed subspace spanned by vectors deemed to be helpful in accelerating convergence or conveying knowledge
of the solution. Recently, a survey was published, in which a framework describing the vast majority of such methods was proposed
[Soodhalter et al., GAMM-Mitt., 43 (2020),
Art. e202000016].
In many of these methods, the Krylov subspace is one generated by the system matrix composed with a projector
that depends on the augmentation space. However, it is not a requirement that a projected Krylov subspace be used. There are augmentation
methods built on using Krylov subspaces generated by the original system matrix, and these methods also fit into the general framework.
In this note, we observe that one gains implementation benefits by considering such augmentation methods with unprojected Krylov subspaces
in the general framework. We demonstrate this
by applying the idea to the R
Full Text (PDF) [584 KB], BibTeX , DOI: 10.1553/etna_vol55s532
Key words
Krylov subspaces, augmentation, recycling, discrete ill-posed problems
AMS subject classifications
65F10, 65F50, 65F08
Links to the cited ETNA articles
| [7] |
Vol. 42 (2014), pp. 136-146 Yiqiu Dong, Henrik Garde, and Per Christian Hansen:
R |
| [13] | Vol. 39 (2012), pp. 156-185 Martin H. Gutknecht: Spectral deflation in Krylov solvers: a theory of coordinate space based methods |
| [24] | Vol. 54 (2021), pp. 256-275 Ronny Ramlau and Bernadett Stadler: An augmented wavelet reconstructor for atmospheric tomography |