Geodesic
On moment methods in Krylov subspaces
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 495 (2020), pp. 38-43 Cet article a éte moissonné depuis la source Math-Net.Ru

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Moment methods in Krylov subspaces for solving symmetric systems of linear algebraic equations (SLAEs) are considered. A family of iterative algorithms is proposed based on generalized Lanczos orthogonalization with an initial vector $v^0$ chosen regardless of the initial residual. By applying this approach, a series of SLAEs with the same matrix, but with different right-hand sides can be solved using a single set of basis vectors. Additionally, it is possible to implement generalized moment methods that reduce to block Krylov algorithms using a set of linearly independent guess vectors $v^0,\dots,v^0_m$. The performance of algorithm implementations is improved by reducing the number of matrix multiplications and applying efficient parallelization of vector operations. It is shown that the applicability of moment methods can be extended using preconditioning to various classes of algebraic systems: indefinite, incompatible, asymmetric, and complex, including non-Hermitian ones.
Keywords: moment method, Krylov subspace, parametric Lanczos orthogonalization, conjugate direction algorithms. 
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     author = {V. P. Il'in},
     title = {On moment methods in {Krylov} subspaces},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {38--43},
     year = {2020},
     volume = {495},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_495_a8/}
}
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V. P. Il'in. On moment methods in Krylov subspaces. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 495 (2020), pp. 38-43. http://geodesic.mathdoc.fr/item/DANMA_2020_495_a8/

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