On the Conjugate Direction Methods With Preconditioning Projectors

V.P. Ilyin

Postal Address: Institute of Computational Mathematics & Mathematical Geophysics, SBRAS, Intel Novosibirsk Laboratory, Lavrentieva ave.,6/1 , Novosibirsk, 630090, Russia

The various types of conjugate and semi-conjugate direction methods are applied for acceleration of iterative processes with preconditioning projectors of multiplicative and additive kinds, proposed by J. Bramble, et all. In particular, we suggest the generalization and further development of row action algorithms, proposed by S.Kaczmarz and G.Cimmino in 30's,and investigated by many authors. The estimations of iterative convergence rate and computational complexity are presented. Variational iterative processes with dynamic preconditioners are considered. The aspects of parallelization and scalability of algorithms are discussed. Results of numerical experiments for representative set of model problems are demonstrated.