Combining the preconditioned conjugate gradient method and a matrix iterative method

Jan Zítko

Applications of Mathematics (1996)

  • Volume: 41, Issue: 1, page 19-39
  • ISSN: 0862-7940

Abstract

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The preconditioned conjugate gradient method for solving the system of linear algebraic equations with a positive definite matrix is investigated. The initial approximation for conjugate gradient is constructed as a result of a matrix iteration method after m steps. The behaviour of the error vector for such a combined method is studied and special numerical tests and conclusions are made.

How to cite

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Zítko, Jan. "Combining the preconditioned conjugate gradient method and a matrix iterative method." Applications of Mathematics 41.1 (1996): 19-39. <http://eudml.org/doc/32935>.

@article{Zítko1996,
abstract = {The preconditioned conjugate gradient method for solving the system of linear algebraic equations with a positive definite matrix is investigated. The initial approximation for conjugate gradient is constructed as a result of a matrix iteration method after $m$ steps. The behaviour of the error vector for such a combined method is studied and special numerical tests and conclusions are made.},
author = {Zítko, Jan},
journal = {Applications of Mathematics},
keywords = {conjugate gradients; preconditioning; iterative method; numerical experiments; error estimation; preconditioned conjugate gradient method; matrix iteration method; numerical examples},
language = {eng},
number = {1},
pages = {19-39},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Combining the preconditioned conjugate gradient method and a matrix iterative method},
url = {http://eudml.org/doc/32935},
volume = {41},
year = {1996},
}

TY - JOUR
AU - Zítko, Jan
TI - Combining the preconditioned conjugate gradient method and a matrix iterative method
JO - Applications of Mathematics
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 1
SP - 19
EP - 39
AB - The preconditioned conjugate gradient method for solving the system of linear algebraic equations with a positive definite matrix is investigated. The initial approximation for conjugate gradient is constructed as a result of a matrix iteration method after $m$ steps. The behaviour of the error vector for such a combined method is studied and special numerical tests and conclusions are made.
LA - eng
KW - conjugate gradients; preconditioning; iterative method; numerical experiments; error estimation; preconditioned conjugate gradient method; matrix iteration method; numerical examples
UR - http://eudml.org/doc/32935
ER -

References

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  12. Improving the Convergence of Iterative Methods, Apl. Mat. 28 (1983), 215–229. (1983) MR0701740
  13. Convergence of Extrapolation Coefficients, , Apl. Mat. 29 (1984), 114–133. (1984) MR0738497
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  15. Combining the preconditioned conjugate gradient method and the norm-reducing matrix iterative method, Technical report No 106/93, Prague 1993, pp. 1–17. 

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