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. Clark, M. A.; Babich, R.; Barros, K.; Brower, R. C.; Rebbi, C.: Solving lattice QCD systems of equations using mixed precision solvers on GPUs (2010)
  2. Oskooi, Ardavan F.; Roundy, David; Ibanescu, Mihai; Bermel, Peter; Joannopoulos, J. D.; Johnson, Steven G.: \textttMEEP: a flexible free-software package for electromagnetic simulations by the FDTD method (2010)
  3. Simoncini, Valeria; Szyld, Daniel B.: Interpreting IDR as a Petrov-Galerkin method (2010)
  4. Sleijpen, Gerard L. G.; Sonneveld, Peter; van Gijzen, Martin B.: Bi-CGSTAB as an induced dimension reduction method (2010)
  5. Tal-Ezer, Hillel; Turkel, Eli: The iterative solver Risolv with application to the exterior Helmholtz problem (2010)
  6. Graves-Morris, P. R.: VPAStab((J,L)): an iterative method with look-ahead for the solution of large sparse linear systems (2009)
  7. van der Vorst, Henk A.: Iterative Krylov methods for large linear systems (2009)
  8. Abe, Kuniyoshi; Zhang, Shao-Liang: A variant algorithm of the Orthomin((m)) method for solving linear systems (2008)
  9. Macklin, Paul; Lowengrub, John S.: A new ghost cell/level set method for moving boundary problems: application to tumor growth (2008)
  10. Didier, Eric; Borges, António: Numerical predictions of low Reynolds number flow over an oscillating circular cylinder flow past an oscillating cylinder (2007)
  11. Graves-Morris, P. R.: BiCGStab, VPAStab and an adaptation to mildly nonlinear systems (2007)
  12. Gutknecht, Martin H.: A brief introduction to Krylov space methods for solving linear systems (2007)
  13. Simoncini, Valeria; Szyld, Daniel B.: Recent computational developments in Krylov subspace methods for linear systems. (2007)
  14. Meurant, Gérard; Strakoš, Zdenek: The Lanczos and conjugate gradient algorithms in finite precision arithmetic (2006)
  15. Smith, Ian M.; Margetts, Lee: The convergence variability of parallel iterative solvers (2006)
  16. Venturino, E.; Graves-Morris, P. R.; De Rossi, A.: An adaptation of BiCGSTAB for nonlinear biological systems (2006)
  17. Ledger, P. D.; Morgan, K.; Hassan, O.: Frequency and time domain electromagnetic scattering simulations employing higher order edge elements (2005)
  18. Strakoš, Zdeněk; Tichý, Petr: Error estimation in preconditioned conjugate gradients (2005)
  19. van den Eshof, Jasper; Sleijpen, Gerard L. G.; van Gijzen, Martin B.: Iterative linear system solvers with approximate matrix-vector products (2005)
  20. van den Eshof, Jasper; Sleijpen, Gerard L. G.; van Gijzen, Martin B.: Relaxation strategies for nested Krylov methods (2005)