Abstract
In Krylov-based iterative methods, the computation of an orthonormal basis of the Krylov space is a key issue in the algorithms because the many scalar products are often a bottleneck in parallel distributed environments. Using GMRES, we present a comparison of four variants of the Gram-Schmidt process on distributed memory machines. Our experiments are carried on an application in astrophysics and on a convection-diffusion example. We show that the iterative classical Gram-Schmidt method overcomes its three competitors in speed and in parallel scalability while keeping robust numerical properties.
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© 1998 Springer-Verlag Berlin Heidelberg
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Frayssé, V., Giraud, L., Kharraz-Aroussi, H. (1998). On the influence of the orthogonalization scheme on the parallel performance of GMRES. In: Pritchard, D., Reeve, J. (eds) Euro-Par’98 Parallel Processing. Euro-Par 1998. Lecture Notes in Computer Science, vol 1470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0057927
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DOI: https://doi.org/10.1007/BFb0057927
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