Propagation of errors in dynamic iterative schemes

Zubik-Kowal, Barbara

  • Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 97-106

Abstract

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We consider iterative schemes applied to systems of linear ordinary differential equations and investigate their convergence in terms of magnitudes of the coefficients given in the systems. We address the question of whether the reordering of equations in a given system improves the convergence of an iterative scheme.

How to cite

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Zubik-Kowal, Barbara. "Propagation of errors in dynamic iterative schemes." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 97-106. <http://eudml.org/doc/294941>.

@inProceedings{Zubik2017,
abstract = {We consider iterative schemes applied to systems of linear ordinary differential equations and investigate their convergence in terms of magnitudes of the coefficients given in the systems. We address the question of whether the reordering of equations in a given system improves the convergence of an iterative scheme.},
author = {Zubik-Kowal, Barbara},
booktitle = {Proceedings of Equadiff 14},
keywords = {Dynamic iterations, waveform relaxation, Gauss-Seidel schemes, convergence, error bounds},
location = {Bratislava},
pages = {97-106},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {Propagation of errors in dynamic iterative schemes},
url = {http://eudml.org/doc/294941},
year = {2017},
}

TY - CLSWK
AU - Zubik-Kowal, Barbara
TI - Propagation of errors in dynamic iterative schemes
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 97
EP - 106
AB - We consider iterative schemes applied to systems of linear ordinary differential equations and investigate their convergence in terms of magnitudes of the coefficients given in the systems. We address the question of whether the reordering of equations in a given system improves the convergence of an iterative scheme.
KW - Dynamic iterations, waveform relaxation, Gauss-Seidel schemes, convergence, error bounds
UR - http://eudml.org/doc/294941
ER -

References

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  1. Butcher, J. C., Numerical Methods for Ordinary Differential Equations, , Second edition, John Wiley & Sons, Ltd., Chichester, 2008. MR2401398
  2. Burrage, K., Parallel and Sequential Methods for Ordinary Differential Equations, , Oxford University Press, Oxford, 1995. MR1367504
  3. Miekkala, U., Nevanlinna, O., Convergence of dynamic iteration methods for initial value problems, , SIAM J. Sci. Stat. Comput. 8 (1987), pp. 459–482. MR0892300
  4. Miekkala, U., Nevanlinna, O., Iterative solution of systems of linear differential equations, , Acta Numerica (1996), pp. 259–307. MR1624607
  5. Zubik-Kowal, B., Improving the convergence of iterative schemes, , in preparation. 

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