Summary
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 this and similar 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 on this issue and try to provide insight into why some iterative system solvers are more sensitive than others.
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© 2005 Springer-Verlag Berlin Heidelberg
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van den Eshof, J., Sleijpen, G.L., van Gijzen, M.B. (2005). Iterative Linear System Solvers with Approximate Matrix-vector Products. In: Bori~i, A., Frommer, A., Joó, B., Kennedy, A., Pendleton, B. (eds) QCD and Numerical Analysis III. Lecture Notes in Computational Science and Engineering, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28504-0_13
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DOI: https://doi.org/10.1007/3-540-28504-0_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21257-7
Online ISBN: 978-3-540-28504-5
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