Geodesic
Acceleration of the line-by-line recurretnt method in Krylov subspaces
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2011), pp. 45-54

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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.
Keywords: difference elliptic equations, iterative method, Krylov subspaces, line-by-line recurrent method. 
@article{VTGU_2011_2_a5,
     author = {A. A. Fomin and L. N. Fomina},
     title = {Acceleration of the line-by-line recurretnt method in {Krylov} subspaces},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {45--54},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2011_2_a5/}
}
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A. A. Fomin; L. N. Fomina. Acceleration of the line-by-line recurretnt method in Krylov subspaces. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 2 (2011), pp. 45-54. http://geodesic.mathdoc.fr/item/VTGU_2011_2_a5/