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 95 articles , 1 standard article )

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  1. Aihara, Kensuke: Variants of the groupwise update strategy for short-recurrence Krylov subspace methods (2017)
  2. Engwer, Christian; Johannsen, Klaus; Nüßing, Andreas: Algebraic multigrid for discontinuous Galerkin methods using local transformations (2016)
  3. Gu, Xian-Ming; Huang, Ting-Zhu; Carpentieri, Bruno: BiCGCR2: A new extension of conjugate residual method for solving non-Hermitian linear systems (2016)
  4. 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)
  5. Liu, Hui; Wang, Kun; Chen, Zhangxin: A family of constrained pressure residual preconditioners for parallel reservoir simulations. (2016)
  6. 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)
  7. Ahuja, Kapil; Benner, Peter; de Sturler, Eric; Feng, Lihong: Recycling BiCGSTAB with an application to parametric model order reduction (2015)
  8. 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)
  9. 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)
  10. Amritkar, Amit; de Sturler, Eric; Świrydowicz, Katarzyna; Tafti, Danesh; Ahuja, Kapil: Recycling Krylov subspaces for CFD applications and a new hybrid recycling solver (2015)
  11. Götschel, Sebastian; Weiser, Martin: Lossy compression for PDE-constrained optimization: adaptive error control (2015)
  12. Gu, Xian-Ming; Clemens, Markus; Huang, Ting-Zhu; Li, Liang: The CBiCG class of algorithms for complex symmetric linear systems with applications in several electromagnetic model problems (2015)
  13. Huang, Yu-Mei: On $m$-step Hermitian and skew-Hermitian splitting preconditioning methods (2015)
  14. Aihara, Kensuke; Abe, Kuniyoshi; Ishiwata, Emiko: A variant of IDRstab with reliable update strategies for solving sparse linear systems (2014)
  15. Filelis-Papadopoulos, Christos K.; Gravvanis, George A.: Generic approximate sparse inverse matrix techniques (2014)
  16. Güttel, Stefan; Pestana, Jennifer: Some observations on weighted GMRES (2014)
  17. Petra, Cosmin G.; Schenk, Olaf; Lubin, Miles; Gäertner, Klaus: An augmented incomplete factorization approach for computing the Schur complement in stochastic optimization (2014)
  18. 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)
  19. Yeung, Man-Chung: ML($n$)BiCGStabt: a ML($n$)BiCGStab variant with $\bold A$-transpose (2014)
  20. Zhang, Li-Tao: A new preconditioner for generalized saddle point matrices with highly singular $(1,1)$ blocks (2014)

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