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Name:
Miloslav Znojil
Reviewer number:
9689
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE 0151 98 483
Author(s):
Bertaccini, D.:
Shorttitle:
A circulant preconditioner for LMF-based ODE codes
Source:
SIAM J. Sci. Comput. 22, No. 3, 767 - 786 (2000).
Classification:
Primary Classification:
65L05Initial value problems
Secondary Classification:
65F10Iterative methods for linear systems
15A12Conditioning of matrices
Keywords:
ordinary differential equations; implicit linear multistep formulas; boundary value methods; block unsymmetric Toeplitz lionear systems; circulant preconditioning
Review:

With the emphasis on possible practical applications to ordinary
differential equations (solved via implicit formulas and, in this
setting, via reduction to a large and unsymmetric sparse linear
problem in each integration step) a proposal is made that the
preconditioner should be chosen in a block circulant form. Special
attention is paid to the linear multistep formula techniques
leading to the band (and unsymmetric) Toeplitz structures of
matrices. The preference is then recommended of the so called
P-circulant preconditioners. The knowledge of their spectal
properties simplifies the abstract analysis of convergence,
confirmed persuasively by numerical tests.
Remarks to the editors:

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