Świrydowicz, Katarzyna; Langou, Julien; Ananthan, Shreyas; Yang, Ulrike; Thomas, Stephen Low synchronization Gram-Schmidt and generalized minimal residual algorithms. (English) Zbl 1474.65103 Numer. Linear Algebra Appl. 28, No. 2, e2343, 20 p. (2021). 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 Cited in 1 ReviewCited in 5 Documents MSC: 65F25 Orthogonalization in numerical linear algebra 65F10 Iterative numerical methods for linear systems 65Y05 Parallel numerical computation Keywords:massively parallel computers; graphics processing unit; Gram-Schmidt orthogonalization process; Krylov subspace methods; scalable GMRES algorithm; WY compact representation Software:BoomerAMG; CUBLAS; CUDA; CUSPARSE; Matlab; hypre; SparseMatrix PDFBibTeX XMLCite \textit{K. Świrydowicz} et al., Numer. Linear Algebra Appl. 28, No. 2, e2343, 20 p. (2021; Zbl 1474.65103) Full Text: DOI