# On the preconditioned biconjugate gradients for solving linear complex equations arising from finite elements

Michal Křížek; Jaroslav Mlýnek

Banach Center Publications (1994)

- Volume: 29, Issue: 1, page 195-205
- ISSN: 0137-6934

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topKřížek, Michal, and Mlýnek, Jaroslav. "On the preconditioned biconjugate gradients for solving linear complex equations arising from finite elements." Banach Center Publications 29.1 (1994): 195-205. <http://eudml.org/doc/262752>.

@article{Křížek1994,

abstract = {The paper analyses the biconjugate gradient algorithm and its preconditioned version for solving large systems of linear algebraic equations with nonsingular sparse complex matrices. Special emphasis is laid on symmetric matrices arising from discretization of complex partial differential equations by the finite element method.},

author = {Křížek, Michal, Mlýnek, Jaroslav},

journal = {Banach Center Publications},

keywords = {conjugate gradient method; large linear system; finite element; iterative method; preconditioning},

language = {eng},

number = {1},

pages = {195-205},

title = {On the preconditioned biconjugate gradients for solving linear complex equations arising from finite elements},

url = {http://eudml.org/doc/262752},

volume = {29},

year = {1994},

}

TY - JOUR

AU - Křížek, Michal

AU - Mlýnek, Jaroslav

TI - On the preconditioned biconjugate gradients for solving linear complex equations arising from finite elements

JO - Banach Center Publications

PY - 1994

VL - 29

IS - 1

SP - 195

EP - 205

AB - The paper analyses the biconjugate gradient algorithm and its preconditioned version for solving large systems of linear algebraic equations with nonsingular sparse complex matrices. Special emphasis is laid on symmetric matrices arising from discretization of complex partial differential equations by the finite element method.

LA - eng

KW - conjugate gradient method; large linear system; finite element; iterative method; preconditioning

UR - http://eudml.org/doc/262752

ER -

## References

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- [11] B. N. Parlett, D. R. Taylor and Z. A. Liu, A look-ahead Lanczos algorithm for symmetric matrices, Math. Comp. 44 (1985), 105-124. Zbl0564.65022
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- [13] R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1962.
- [14] H. A. van der Vorst and K. Dekker, Conjugate gradient type methods and preconditioning, J. Comput. Appl. Math. 24 (1988), 73-87. Zbl0659.65033
- [15] O. Widlund, A Lanczos method for a class of nonsymmetric systems of linear equations, SIAM J. Numer. Anal. 15 (1978), 801-812. Zbl0398.65030

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