Preconditioning of conjugate gradients by multigrid solver

Jitka Křížková; Petr Vaněk

Applications of Mathematics (1994)

  • Volume: 39, Issue: 5, page 357-364
  • ISSN: 0862-7940

Abstract

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Solving a system of linear algebraic equations by the preconditioned conjugate gradient method requires to solve an auxiliary system of linear algebraic equations in each step. In this paper instead of solving the auxiliary system one iteration of the two level method for the original system is done.

How to cite

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Křížková, Jitka, and Vaněk, Petr. "Preconditioning of conjugate gradients by multigrid solver." Applications of Mathematics 39.5 (1994): 357-364. <http://eudml.org/doc/32890>.

@article{Křížková1994,
abstract = {Solving a system of linear algebraic equations by the preconditioned conjugate gradient method requires to solve an auxiliary system of linear algebraic equations in each step. In this paper instead of solving the auxiliary system one iteration of the two level method for the original system is done.},
author = {Křížková, Jitka, Vaněk, Petr},
journal = {Applications of Mathematics},
keywords = {conjugate gradient method; preconditioning; multigrid method; multigrid method; preconditioned conjugate gradient method; two level method},
language = {eng},
number = {5},
pages = {357-364},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Preconditioning of conjugate gradients by multigrid solver},
url = {http://eudml.org/doc/32890},
volume = {39},
year = {1994},
}

TY - JOUR
AU - Křížková, Jitka
AU - Vaněk, Petr
TI - Preconditioning of conjugate gradients by multigrid solver
JO - Applications of Mathematics
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 5
SP - 357
EP - 364
AB - Solving a system of linear algebraic equations by the preconditioned conjugate gradient method requires to solve an auxiliary system of linear algebraic equations in each step. In this paper instead of solving the auxiliary system one iteration of the two level method for the original system is done.
LA - eng
KW - conjugate gradient method; preconditioning; multigrid method; multigrid method; preconditioned conjugate gradient method; two level method
UR - http://eudml.org/doc/32890
ER -

References

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  1. Adaptive Iterative Solvers in Finite Elements, (to appear). (to appear) 
  2. 10.1002/cnm.1640090307, Communications in numerical methods in engineering, vol. 9 (1993). Zbl1071.65558MR1208381DOI10.1002/cnm.1640090307
  3. Introduction to Linear and Nonlinear Programming, Addison-Wesley, New York, 1973. (1973) Zbl0297.90044
  4. Iterative Methods for Numerical Solving of the Boundary Value Problems of Elasticity, Thesis, Ostrava, 1989. (Czech) (1989) 
  5. Acceleration of Algebraic Multigrid Method, Proceedings of the IXth Summer School SANM, 1991. (1991) 
  6. Multigrid Methods and Applications, Springer Verlag, 1985. (1985) MR0814495
  7. The Acceleration of the Convergence of a Two-level Algebraic Algorithm by Aggregation in Smoothing Process, Applications of Math. 37 (1992), no. 5. (1992) MR1175929
  8. Finite Element Solution of Boundary Value Problems, Academic Press, 1984. (1984) MR0758437

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