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. Vincent, Stéphane; Brändle de Motta, Jorge César; Sarthou, Arthur; Estivalezes, Jean-Luc; Simonin, Olivier; Climent, Eric: A Lagrangian VOF tensorial penalty method for the DNS of resolved particle-laden flows (2014)
  2. Yeung, Man-Chung: ML((n))BiCGStabt: a ML((n))BiCGStab variant with (\mathbfA)-transpose (2014)
  3. Zhang, Li-Tao: A new preconditioner for generalized saddle point matrices with highly singular ((1,1)) blocks (2014)
  4. Zhu, Sheng-Xin; Gu, Tong-Xiang; Liu, Xing-Ping: Minimizing synchronizations in sparse iterative solvers for distributed supercomputers (2014)
  5. Abe, Kuniyoshi; Sleijpen, Gerard L. G.: Solving linear equations with a stabilized GPBiCG method (2013)
  6. Bai, Zhong-Zhi; Ren, Zhi-Ru: Block-triangular preconditioning methods for linear third-order ordinary differential equations based on reduced-order sinc discretizations (2013)
  7. Gedela, Satyanarayana; Sundar, S.: A numerical study of hierarchical matrix ((\mathcalH)-matrix) for finite point set method (FPM) on solving a Poisson problem (2013)
  8. Liang, Yu; Szularz, Marek; Yang, Laurence T.: Finite-element-wise domain decomposition iterative solvers with polynomial preconditioning (2013)
  9. Rendel, Olaf; Rizvanolli, Anisa; Zemke, Jens-Peter M.: IDR: a new generation of Krylov subspace methods? (2013)
  10. Theillard, Maxime; Djodom, Landry Fokoua; Vié, Jean-Léopold; Gibou, Frédéric: A second-order sharp numerical method for solving the linear elasticity equations on irregular domains and adaptive grids -- application to shape optimization (2013)
  11. Abe, Kuniyoshi; Sleijpen, Gerard L. G.: Hybrid Bi-CG methods with a Bi-CG formulation closer to the IDR approach (2012)
  12. Banjai, Lehel; Peterseim, Daniel: Parallel multistep methods for linear evolution problems (2012)
  13. Erlangga, Yogi; Turkel, Eli: Iterative schemes for high order compact discretizations to the exterior Helmholtz equation (2012)
  14. Kapellos, George E.; Alexiou, Terpsichori S.; Payatakes, Alkiviades C.: A multiscale theoretical model for fluid flow in cellular biological media (2012)
  15. Sonneveld, Peter: On the convergence behavior of IDR((s)) and related methods (2012)
  16. Fischer, Bernd: Polynomial based iteration methods for symmetric linear systems (2011)
  17. Knibbe, H.; Oosterlee, C. W.; Vuik, C.: GPU implementation of a Helmholtz Krylov solver preconditioned by a shifted Laplace multigrid method (2011)
  18. Abe, Kuniyoshi; Sleijpen, Gerard L. G.: BiCR variants of the hybrid BiCG methods for solving linear systems with nonsymmetric matrices (2010)
  19. Alavani, Chitra; Glowinski, Roland; Gomez, Susana; Ivorra, Benjamin; Joshi, Pallavi; Ramos, Angel Manuel: Modelling and simulation of a polluted water pumping process (2010)
  20. Bogachev, K. Yu.; Mikhaleva, M. Yu.; Gorelov, I. G.: Algebraic multilevel method AMG: comparison with the method BICGSTAB + ILU and its use in the method CPR (2010)