BiCGstab

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. Abe, Kuniyoshi; Zhang, Shao-Liang; Mitsui, Taketomo; Jin, Cheng-Hai: A variant of the ORTHOMIN(2) method for singular linear systems (2004)
  2. van den Eshof, Jasper; Sleijpen, Gerard L. G.: Accurate conjugate gradient methods for families of shifted systems (2004)
  3. van den Eshof, Jasper; Sleijpen, Gerard L. G.: Inexact Krylov subspace methods for linear systems (2004)
  4. Ginzburg, I.; Wittum, G.; Zaleski, S.: Adaptive multigrid computations of multiphase flows (2003)
  5. Strakoš, Zdeněk; Tichý, Petr: On error estimation in the conjugate gradient method and why it works in finite precision computations (2002)
  6. van den Eshof, J.; Frommer, A.; Lippert, Th.; Schilling, K.; van der Vorst, H. A.: Numerical methods for the QCDd overlap operator. I: Sign-function and error bounds (2002)
  7. van der Vorst, Henk A.: Efficient and reliable iterative methods for linear systems (2002)
  8. Deng, G. B.; Piquet, J.; Vasseur, X.; Visonneau, M.: A new fully coupled method for computing turbulent flows (2001)
  9. Ginzburg, I.; Wittum, G.: Two-phase flows on interface refined grids modeled with VOF, staggered finite volumes, and spline interpolants (2001)
  10. Gutknecht, Martin H.; Rozložnik, Miroslav: Residual smoothing techniques: Do they improve the limiting accuracy of iterative solvers? (2001)
  11. Wong, J. S.; Darmofal, D. L.; Peraire, J.: The solution of the compressible Euler equations at low Mach numbers using a stabilized finite element algorithm (2001)
  12. Bai, Zhaojun (ed.); Demmel, James (ed.); Dongarra, Jack (ed.); Ruhe, Axel (ed.); Van der Vorst, Henk (ed.): Templates for the solution of algebraic eigenvalue problems. A practical guide (2000)
  13. Bertaccini, D.: A circulant preconditioner for the systems of LMF-based ODE codes (2000)
  14. Gutknecht, Martin H.: On Lanczos-type methods for Wilson fermions (2000)
  15. Gutknecht, Martin H.; Ressel, Klaus J.: Look-ahead procedures for Lanczos-type product methods based on three-term Lanczos recurrences (2000)
  16. Gutknecht, Martin H.; Strakos, Zdenvek: Accuracy of two three-term and three two-term recurrences for Krylov space solvers (2000)
  17. Sleijpen, Gerard L. G.; Van der Vorst, Henk A.; Modersitzki, Jan: Differences in the effects of rounding errors in Krylov solvers for symmetric indefinite linear systems (2000)
  18. van der Vorst, Henk A.; Ye, Qiang: Residual replacement strategies for Krylov subspace iterative methods for the convergence of true residuals (2000)
  19. Botta, E. F. F.; Wubs, F. W.: Matrix renumbering ILU: An effective algebraic multilevel ILU preconditioner for sparse matrices (1999)
  20. Chan, Tony F.; de Pillis, Lisette; van der Vorst, Henk: Transpose-free formulations of Lanczos-type methods for nonsymmetric linear systems (1998)