On condition numbers of symmetric and nonsymmetric domain decomposition methods

05/30/2019

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by   Juan Galvis, et al.

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Using oblique projections and angles between subspaces we write condition number estimates for abstract nonsymmetric domain decomposition methods. In particular, we design and estimate the condition number of restricted additive Schwarz methods. We also obtain non-negativity of the pre-conditioner operator. Condition number estimates are not enough for the convergence of iterative method such as GMRES but these bounds may lead to further understanding of restricted methods.