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. Liu, Hui; Wang, Kun; Chen, Zhangxin: A family of constrained pressure residual preconditioners for parallel reservoir simulations. (2016)
  2. 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)
  3. Ahuja, Kapil; Benner, Peter; de Sturler, Eric; Feng, Lihong: Recycling BiCGSTAB with an application to parametric model order reduction (2015)
  4. 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)
  5. 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)
  6. Amritkar, Amit; de Sturler, Eric; Świrydowicz, Katarzyna; Tafti, Danesh; Ahuja, Kapil: Recycling Krylov subspaces for CFD applications and a new hybrid recycling solver (2015)
  7. Bertolazzi, Enrico; Frego, Marco: Preconditioning complex symmetric linear systems (2015)
  8. Chertovskih, R.; Zheligovsky, V.: Large-scale weakly nonlinear perturbations of convective magnetic dynamos in a rotating layer (2015)
  9. Götschel, Sebastian; Weiser, Martin: Lossy compression for PDE-constrained optimization: adaptive error control (2015)
  10. 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)
  11. Huang, Yu-Mei: On (m)-step Hermitian and skew-Hermitian splitting preconditioning methods (2015)
  12. van Gijzen, Martin B.; Sleijpen, Gerard L. G.; Zemke, Jens-Peter M.: Flexible and multi-shift induced dimension reduction algorithms for solving large sparse linear systems. (2015)
  13. Aihara, Kensuke; Abe, Kuniyoshi; Ishiwata, Emiko: A variant of IDRstab with reliable update strategies for solving sparse linear systems (2014)
  14. Ballard, G.; Carson, E.; Demmel, J.; Hoemmen, M.; Knight, N.; Schwartz, O.: Communication lower bounds and optimal algorithms for numerical linear algebra (2014)
  15. Chen, Zhangxin; Liu, Hui; Yu, Song; Hsieh, Ben; Shao, Lei: GPU-based parallel reservoir simulators (2014)
  16. Filelis-Papadopoulos, Christos K.; Gravvanis, George A.: Generic approximate sparse inverse matrix techniques (2014)
  17. Güttel, Stefan; Pestana, Jennifer: Some observations on weighted GMRES (2014)
  18. Petra, Cosmin G.; Schenk, Olaf; Lubin, Miles; Gäertner, Klaus: An augmented incomplete factorization approach for computing the Schur complement in stochastic optimization (2014)
  19. Saito, Shusaku; Tadano, Hiroto; Imakura, Akira: Development of the block BiCGSTAB((\ell)) method for solving linear systems with multiple right hand sides (2014)
  20. Sun, Dong-Lin; Jing, Yan-Fei; Huang, Ting-Zhu; Carpentieri, Bruno: A quasi-minimal residual variant of the BiCORSTAB method for nonsymmetric linear systems (2014)