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Variants of the groupwise update strategy for short-recurrence Krylov subspace methods. (English) Zbl 1368.65046
Summary: Krylov subspace methods often use short-recurrences for updating approximations and the corresponding residuals. In the bi-conjugate gradient (Bi-CG) type methods, rounding errors arising from the matrix-vector multiplications used in the recursion formulas influence the convergence speed and the maximum attainable accuracy of the approximate solutions. The strategy of a groupwise update has been proposed for improving the convergence of the Bi-CG type methods in finite-precision arithmetic. In the present paper, we analyze the influence of rounding errors on the convergence properties when using alternative recursion formulas, such as those used in the bi-conjugate residual (Bi-CR) method, which are different from those used in the Bi-CG type methods. We also propose variants of a groupwise update strategy for improving the convergence speed and the accuracy of the approximate solutions. Numerical experiments demonstrate the effectiveness of the proposed method.

65F10 Iterative numerical methods for linear systems
Full Text: DOI
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