Acceleration of the line-by-line recurretnt method in Krylov subspaces

Two techniques of acceleration of line-by-line recurrent method in Krylov subspaces are considered by the example of the LR1 algorithm. The van der Vorst Bi-CGStab P algorithm is used as an accelerating method. It is shown that the traditional approach (generation of a preconditioner on the base of LR1 algorithm) doesn't yield the required result. At the same time, the direct combination of LR1 and Bi-CGStab P algorithms allows to raise the convergence speed considerably.