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1994 | 29 | 1 | 195-205
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
29
Numer
1
Strony
195-205
Opis fizyczny
Daty
wydano
1994
Twórcy
  • Matematický ústav AV ČR, Žitná 25, 11567 Praha 1, Czech Republic
  • Matematický ústav AV ČR, Žitná 25, 11567 Praha 1, Czech Republic
Bibliografia
  • [1] O. Axelsson and V. A. Barker, Finite Element Solution of Boundary Value Problems. Theory and Computation, Academic Press, New York 1984.
  • [2] F. S. Beckman, The solution of linear equations by the conjugate gradient method, in: Mathematical Methods for Digital Computers, A. Ralston and H. S. Wilf (eds.), Wiley, New York 1960, 62-72.
  • [3] R. Fletcher, Conjugate gradient methods for indefinite systems, in: Proc. Dundee Conf. on Numerical Analysis, A. Dold and B.Eckmann (eds.), Lecture Notes in Math. 506, Springer, New York 1975, 73-89.
  • [4] R. W. Freund, Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices, SIAM J. Sci. Statist. Comput. 13 (1992), 1-23.
  • [5] R. W. Freund and N. M. Nachtigal, QMR: a quasi-minimal residual method for non-Hermitian linear systems, RIACS Technical Report 90.51, NASA, Columbia 1990, 33 pp.
  • [6] D. A. H. Jacobs, A generalization of the conjugate-gradient method to solve complex systems, IMA J. Numer. Anal. 6 (1986), 447-452.
  • [7] A. Kiełbasiński, Catalogue of linear algebra algorithms of the journal Numerische Mathematik, Mat. Stos. 2 (1974), 5-13 (in Polish).
  • [8] M. Křížek and P. Neittaanmäki, Finite Element Approximation of Variational Problems and Applications, Longman, Harlow 1990.
  • [9] D. G. Luenberger, Hyperbolic pairs in the conjugate gradients, SIAM J. Appl. Math. 17 (1969), 1263-1267.
  • [10] Z. Mikić and E. C. Morse, The use of a preconditioned bi-conjugate gradient method for hybrid plasma stability analysis, J. Comput. Phys. 61 (1985), 154-185.
  • [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.
  • [12] Y. Saad, The Lanczos biorthogonalization algorithm and other oblique projection methods for solving large unsymmetric systems, SIAM J. Numer. Anal. 19 (1982), 485-506.
  • [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.
  • [15] O. Widlund, A Lanczos method for a class of nonsymmetric systems of linear equations, SIAM J. Numer. Anal. 15 (1978), 801-812.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv29z1p195bwm
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