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Collignon, T.P. (author), Sleijpen, G.L.G. (author), Van Gijzen, M.B. (author)In this paper the IDR(s) method is interpreted in the context of deflation methods. It is shown that IDR(s) can be seen as a Richardson iteration preconditioned by a variable deflation–type preconditioner. The main result of this paper is the IDR projection theorem, which relates the spectrum of the deflated system in each IDR(s) cycle to all...report 2010
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Van Gijzen, M.B. (author), Collignon, T.P. (author)The IDR(s) method that is proposed in [26] is an efficient limited memory method for solving large nonsymmetric systems of linear equations. In [11] an IDR(s) variant is described that has a single synchronisation point per iteration step, which makes this variant well-suited for parallel and grid computing. In this paper, we combine this IDR(s)...report 2010
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Collignon, T.P. (author), Van Gijzen, M.B. (author)IDR(s) is a family of fast algorithms for iteratively solving large nonsymmetric linear systems [14]. With cluster computing and in particular with Grid computing, the inner product is a bottleneck operation. In this paper, three techniques are combined in order to alleviate this bottleneck. Firstly, the efficient and stable IDR(s) algorithm...report