BiCGstab($l$) and other hybrid Bi-CG methods. Various implementations of the modification BiCGstab(l) of the bi-conjugate gradient method for the solution of a system of linear algebraic equations with a non-singular n×n matrix are studied. The basis of these method forms various investigations of the BiCG part and the polynomial part. The second one is used for further reduction of the BiCG residue and for improving the numerical stability. Both parts are studied in detail. The theory is illustrated by numerical examples.

References in zbMATH (referenced in 119 articles , 1 standard article )

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  1. Klawonn, Axel: Block-triangular preconditioners for saddle point problems with a penalty term (1998)
  2. Klawonn, Axel: An optimal preconditioner for a class of saddle point problems with a penalty term (1998)
  3. Lehoucq, R. B.; Meerbergen, Karl: Using generalized Cayley transformations within an inexact rational Krylov sequence method (1998)
  4. Brezinski, Claude: Projection methods for systems of equations (1997)
  5. Chan, Tony F.; Ye, Qiang: A mixed product Krylov subspace method for solving nonsymmetric linear systems (1997)
  6. Gutknecht, Martin H.: Lanczos-type solvers for nonsymmetric linear systems of equations (1997)
  7. Meerbergen, Karl; Roose, Dirk: The restarted Arnoldi method applied to iterative linear system solvers for the computation of rightmost eigenvalues (1997)
  8. van der Vorst, Henk A.; Chan, Tony F.: Linear system solvers: Sparse iterative methods (1997)
  9. Cullum, Jane: Iterative methods for solving (Ax=b), GMRES/FOM versus QMR/BiCG (1996)
  10. Fokkema, Diederik R.; Sleijpen, Gerard L. G.; Van der Vorst, Henk A.: Generalized conjugate gradient squared (1996)
  11. Sleijpen, G. L. G.; van der Vorst, H. A.: Reliable updated residuals in hybrid Bi-CG methods (1996)
  12. de Sturler, E.; van der Vorst, H. A.: Reducing the effect of global communication in (\textGMRES(m)) and CG on parallel distributed memory computers (1995)
  13. Schönauer, Willi; Weiss, Rüdiger: An engineering approach to generalized conjugate gradient methods and beyond (1995)
  14. Sleijpen, Gerard L. G.; van der Vorst, Henk A.: Maintaining convergence properties of BiCGStab methods in finite precision arithmetic (1995)
  15. Sleijpen, Gerard L. G.; Van der Vorst, Henk A.: Hybrid bi-conjugate gradient methods for CFD problems (1995)
  16. Sleijpen, Gerard L. G.; Van der Vorst, Henk A.: An overview of approaches for the stable computation of hybrid BiCG methods (1995)
  17. Weiss, Rüdiger: A theoretical overview of Krylov subspace methods (1995)
  18. Sleijpen, G. L. G.; van der Vorst, H. A.; Fokkema, D. R.: BiCGstab((l)) and other hybrid Bi-CG methods (1994)
  19. Sonneveld, Peter: CGS, a fast Lanczos-type solver for nonsymmetric linear systems (1989)

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