"Parallel forming of preconditioners based on the approximation of the Sherman-Morrison inversion formula"
Nedozhogin N.S., Kopysov S.P., and Novikov A.K.

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.

  • Nedozhogin N.S. – Institute of Mechanics, Ural Branch of Russian Academy of Sciences; ulitsa Baramzinoi 34, Izhevsk, 426067, Russia; Junior Scientist, e-mail: Negozhogin@inbox.ru
  • Kopysov S.P. – Institute of Mechanics, Ural Branch of Russian Academy of Sciences; ulitsa Baramzinoi 34, Izhevsk, 426067, Russia; Dr. Sci, Professor, Head of Laboratory, e-mail: s.kopysov@gmail.com
  • Novikov A.K. – Institute of Mechanics, Ural Branch of Russian Academy of Sciences; ulitsa Baramzinoi 34, Izhevsk, 426067, Russia; Ph.D., Associate Professor, e-mail: sc_work@mail.ru