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Variants of the groupwise update strategy for short-recurrence Krylov subspace methods.

Authors :
Aihara, Kensuke
Source :
Numerical Algorithms; Jun2017, Vol. 75 Issue 2, p397-412, 16p
Publication Year :
2017

Abstract

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10171398
Volume :
75
Issue :
2
Database :
Complementary Index
Journal :
Numerical Algorithms
Publication Type :
Academic Journal
Accession number :
123225278
Full Text :
https://doi.org/10.1007/s11075-016-0183-y