BiCGstab

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 88 articles , 1 standard article )

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  1. Engwer, Christian; Johannsen, Klaus; Nüßing, Andreas: Algebraic multigrid for discontinuous Galerkin methods using local transformations (2016)
  2. Gu, Xian-Ming; Huang, Ting-Zhu; Carpentieri, Bruno: BiCGCR2: A new extension of conjugate residual method for solving non-Hermitian linear systems (2016)
  3. Liu, Hui; Wang, Kun; Chen, Zhangxin: A family of constrained pressure residual preconditioners for parallel reservoir simulations. (2016)
  4. Ahuja, Kapil; Benner, Peter; de Sturler, Eric; Feng, Lihong: Recycling BiCGSTAB with an application to parametric model order reduction (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. 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)
  7. Götschel, Sebastian; Weiser, Martin: Lossy compression for PDE-constrained optimization: adaptive error control (2015)
  8. 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)
  9. Aihara, Kensuke; Abe, Kuniyoshi; Ishiwata, Emiko: A variant of IDRstab with reliable update strategies for solving sparse linear systems (2014)
  10. Güttel, Stefan; Pestana, Jennifer: Some observations on weighted GMRES (2014)
  11. Petra, Cosmin G.; Schenk, Olaf; Lubin, Miles; Gäertner, Klaus: An augmented incomplete factorization approach for computing the Schur complement in stochastic optimization (2014)
  12. Yeung, Man-Chung: ML($n$)BiCGStabt: a ML($n$)BiCGStab variant with $\bold A$-transpose (2014)
  13. Zhang, Li-Tao: A new preconditioner for generalized saddle point matrices with highly singular $(1,1)$ blocks (2014)
  14. Zhu, Sheng-Xin; Gu, Tong-Xiang; Liu, Xing-Ping: Minimizing synchronizations in sparse iterative solvers for distributed supercomputers (2014)
  15. Abe, Kuniyoshi; Sleijpen, Gerard L.G.: Solving linear equations with a stabilized GPBiCG method (2013)
  16. Bai, Zhong-Zhi; Ren, Zhi-Ru: Block-triangular preconditioning methods for linear third-order ordinary differential equations based on reduced-order sinc discretizations (2013)
  17. Gedela, Satyanarayana; Sundar, S.: A numerical study of hierarchical matrix $(\cal H$-matrix) for finite point set method (FPM) on solving a Poisson problem (2013)
  18. Liang, Yu; Szularz, Marek; Yang, Laurence T.: Finite-element-wise domain decomposition iterative solvers with polynomial preconditioning (2013)
  19. Rendel, Olaf; Rizvanolli, Anisa; Zemke, Jens-Peter M.: IDR: a new generation of Krylov subspace methods? (2013)
  20. 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)

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