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.

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  1. Baumann, M.; Astudillo, R.; Qiu, Y.; Ang, E. Y. M.; van Gijzen, M. B.; Plessix, R.-É.: An MSSS-preconditioned matrix equation approach for the time-harmonic elastic wave equation at multiple frequencies (2018)
  2. Carson, Erin C.: The adaptive (s)-step conjugate gradient method (2018)
  3. Carson, Erin C.; Rozložník, Miroslav; Strakoš, Zdeněk; Tichý, Petr; Tuma, Miroslav: The numerical stability analysis of pipelined conjugate gradient methods: historical context and methodology (2018)
  4. Cools, Siegfried; Yetkin, Emrullah Fatih; Agullo, Emmanuel; Giraud, Luc; Vanroose, Wim: Analyzing the effect of local rounding error propagation on the maximal attainable accuracy of the pipelined conjugate gradient method (2018)
  5. Aihara, Kensuke: Variants of the groupwise update strategy for short-recurrence Krylov subspace methods (2017)
  6. Guérillot, Dominique; Bruyelle, Jérémie: Compositional dual mesh method for single phase flow in heterogeneous porous media -- application to CO(_2) storage (2017)
  7. Monteleone, Alessandra; Monteforte, Massimiliano; Napoli, Enrico: Inflow/outflow pressure boundary conditions for smoothed particle hydrodynamics simulations of incompressible flows (2017)
  8. Zemke, Jens-Peter M.: Variants of IDR with partial orthonormalization (2017)
  9. Astudillo, Reinaldo; van Gijzen, Martin B.: The induced dimension reduction method applied to convection-diffusion-reaction problems (2016)
  10. Engwer, Christian; Johannsen, Klaus; Nüßing, Andreas: Algebraic multigrid for discontinuous Galerkin methods using local transformations (2016)
  11. Gu, Xian-Ming; Huang, Ting-Zhu; Carpentieri, Bruno: BiCGCR2: A new extension of conjugate residual method for solving non-Hermitian linear systems (2016)
  12. Hamilton, Steven; Berrill, Mark; Clarno, Kevin; Pawlowski, Roger; Toth, Alex; Kelley, C. T.; Evans, Thomas; Philip, Bobby: An assessment of coupling algorithms for nuclear reactor core physics simulations (2016)
  13. Liu, Hui; Wang, Kun; Chen, Zhangxin: A family of constrained pressure residual preconditioners for parallel reservoir simulations. (2016)
  14. Luo, Wei-Hua; Huang, Ting-Zhu; Li, Liang; Li, Hou-Biao; Gu, Xian-Ming: Quadratic spline collocation method and efficient preconditioner for the Helmholtz equation with the Sommerfeld boundary conditions (2016)
  15. Ahuja, Kapil; Benner, Peter; de Sturler, Eric; Feng, Lihong: Recycling BiCGSTAB with an application to parametric model order reduction (2015)
  16. Akhunov, R. R.; Kuksenko, S. P.; Gazizov, T. R.: Acceleration of multiple iterative solution of linear algebraic systems in computing the capacitance of a microstrip line in wide ranges of its sizes (2015)
  17. Akhunov, R. R.; Kuksenko, S. P.; Gazizov, T. R.: Multiple solution of systems of linear algebraic equations by an iterative method with recomputed preconditioners (2015)
  18. Amritkar, Amit; de Sturler, Eric; Świrydowicz, Katarzyna; Tafti, Danesh; Ahuja, Kapil: Recycling Krylov subspaces for CFD applications and a new hybrid recycling solver (2015)
  19. Bertolazzi, Enrico; Frego, Marco: Preconditioning complex symmetric linear systems (2015)
  20. Chertovskih, R.; Zheligovsky, V.: Large-scale weakly nonlinear perturbations of convective magnetic dynamos in a rotating layer (2015)

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