Geodesic
Parallel forming of preconditioners based on the approximation of the Sherman-Morrison inversion formula
Numerical methods and programming, Tome 16 (2015) no. 1, pp. 86-93

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Acceleration of preconditioned bi-conjugate gradient stabilized (BiCGStab) methods with preconditioners based on the matrix approximation by the Sherman-Morrison inversion formula is studied. A new form of the parallel algorithm using matrix-vector products to generate preconditioning matrices is proposed. A parallelization efficiency of the most resource-intensive operations of such preconditioners on multi-core central and graphics processing units (CPUs and GPUs) is shown.
Keywords: linear systems, explicit preconditioning, Sherman-Morrison formula, parallel computing, graphics accelerators. 
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     author = {N. S. Nedozhogin and S. P. Kopysov and A. K. Novikov},
     title = {Parallel forming of preconditioners based on the approximation of the {Sherman-Morrison} inversion formula},
     journal = {Numerical methods and programming},
     pages = {86--93},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2015_16_1_a8/}
}
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N. S. Nedozhogin; S. P. Kopysov; A. K. Novikov. Parallel forming of preconditioners based on the approximation of the Sherman-Morrison inversion formula. Numerical methods and programming, Tome 16 (2015) no. 1, pp. 86-93. http://geodesic.mathdoc.fr/item/VMP_2015_16_1_a8/