Abstract
The gradient methods considered are not better than the algorithms based on the minimization of the spectral radius of the transition operator as far as the asymptotic rate of convergence is concerned. At the same time they are somewhat worse as concerns the economy of computation. On the other hand, our opinion is that the bounds and illustrative numerical experiments presented indicate that their efficiency is sufficiently good. Gradient methods possess suitable relaxation properties for small values of n (including also singular matrices). Apparently the nonlinear problem of the choice of parameters τ n from variational considerations needs further investigation.
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© 1979 Spring-Verlag
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Il'in, V. (1979). Gradient alternating-direction methods. In: Fábera, J. (eds) Equadiff IV. Lecture Notes in Mathematics, vol 703. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067269
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DOI: https://doi.org/10.1007/BFb0067269
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