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Low synchronization Gram-Schmidt and generalized minimal residual algorithms. (English) Zbl 1474.65103

The authors focus on a reformulation of orthogonalization algorithms to minimize the number of global reductions and synchronizations. They present low synchronization variants of the classical Gram-Schmidt algorithm with reorthogonalization (CGS2) and modified Gram-Schmidt (MGS) algorithm that require one or two global reduction communication steps. This is done using a novel idea of the compact WY representation of an orthogonal projector where a sequence of elementary projections can be implemented with a triangular solve. Based on that the authors introduce a variant of the MGS GMRES method that is numerically stable and requires only one synchronization per iteration.
Reviewer: Miroslav Rozloznik

MSC:

65F25 Orthogonalization in numerical linear algebra
65F10 Iterative numerical methods for linear systems
65Y05 Parallel numerical computation
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