Iterative linear system solvers with approximate matrix-vector products
Publication date
2003-12
Authors
Eshof, J. van den
Sleijpen, G.L.G.
Gijzen, M.B. van
Editors
Advisors
Supervisors
DOI
Document Type
Preprint
Metadata
Show full item recordCollections
License
Abstract
There are classes of linear problems for which a matrix-vector product is a time
consuming operation because an expensive approximation method is required to
compute it to a given accuracy. One important example is simulations in lattice
QCD with Neuberger fermions where a matrix multiply requires the product of the
matrix sign function of a large sparse matrix times a vector. The recent interest
in these type of applications has resulted in research efforts to study the effect
of errors in the matrix-vector products on iterative linear system solvers. In this
paper we give a very general and abstract discussion of this issue and try to provide
insight into why some iterative system solvers are more sensitive than others.
Preprint 1293, Dep. Math., University Utrecht (December, 2003).
In QCD and Numerical Analysis III, the Proceedings of the Third International Workshop on Numerical Analysis and Lattice QCD, Edinburgh, June/July 2003, Lecture Notes in Computational Science and Engineering, A. Borici, A. Frommer, B. Joo, A.D. Kennedy, and B. Pendleton (Eds), Lecture Notes in Computational Science and Engineering, Vol. 47, 2005, pp. 133-141. Springer-Verlag, Heidelberg, Germany