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Astudillo, R. (author), Van Gijzen, M.B. (author)
This paper discusses the solution of large-scale linear matrix equations using the Induced Dimension reduction method (IDR(s)). IDR(s) was originally presented to solve system of linear equations, and is based on the IDR(s) theorem. We generalize the IDR(s) theorem to solve linear problems in any finite-dimensional space. This generalization...
report 2015
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Sonneveld, P. (author)
An explanation is given of the convergence behavior of IDR(s) methods. The convergence mechanism of these algorithms has two components. The first consists of damping properties of certain factors in the residual polynomials, which becomes less important for large values of s. The second component depends on the behavior of Lanczos polynomials...
journal article 2012
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Sleijpen, G.L.G. (author), Van Gijzen, M.B. (author)
IDR(s) [P. Sonneveld and M. B. van Gijzen, SIAM J. Sci. Comput., 31 (2008), pp. 1035–1062] and BiCGstab(?) [G. L. G. Sleijpen and D. R. Fokkema, Electron. Trans. Numer. Anal., 1 (1993), pp. 11–32] are two of the most efficient short-recurrence iterative methods for solving large nonsymmetric linear systems of equations. Which of the two is best...
journal article 2010