Two-level least squares acceleration approaches are applied to the Chebyshev acceleration method and the restarted conjugate residual method in solving systems of linear algebraic equations with sparse unsymmetric coefficient matrices arising from finite volume or finite element approximations of boundary-value problems on irregular grids. Application of the proposed idea to other iterative restarted processes also is considered. The efficiency of the algorithms suggested is investigated numerically on a set of model Dirichlet problems for the convection-diffusion equation.
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References
Y. Saad, Iterative Methods for Sparse Linear System, PWS Publ. (2002).
V. P. Il’in, Methods and Technologies of Finite Element Methods [in Russian], IVMMG Publ., Novosibirsk (2007).
V. P. Il’in, “Problems of parallel solution of large systems of linear algebraic equations,” Zap. Nauchn. Semin. POMI, 439, 112–127 (2015).
C. L. Lawson and R. Z. Hanson, Solving Least Squares Problems [Russian translation], Nauka, Moscow (1986).
V. P. Il’in, “Least squares methods in Krylov subspaces,” Zap. Nauchn. Semin. POMI, 453, 131–147 (2016).
D. P. O’Leary, “Yet another polynomial preconditioner for the conjugate gradient algorithm,” Linear Algebra Appl., 154-156, 377–388 (1991).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 463, 2017, pp. 224–239.
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Il’in, V.P. Two-Level Least Squares Methods in Krylov Subspaces. J Math Sci 232, 892–902 (2018). https://doi.org/10.1007/s10958-018-3916-8
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DOI: https://doi.org/10.1007/s10958-018-3916-8