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. Terekhov, Kirill M.; Vassilevski, Yuri V.: Finite volume method for coupled subsurface flow problems. II: Poroelasticity (2022)
  2. Xu, Zhuangzhi; Cai, Wenjun; Hu, Dongdong; Wang, Yushun: Exponential integrator preserving mass boundedness and energy conservation for nonlinear Schrödinger equation (2022)
  3. Lin, Xue-lei; Ng, Micheal K.; Wathen, Andy: Preconditioners for multilevel Toeplitz linear systems from steady-state and evolutionary advection-diffusion equations (2021)
  4. Terekhov, Kirill M.: Collocated finite-volume method for the incompressible Navier-Stokes problem (2021)
  5. Carson, Erin Claire: An adaptive (s)-step conjugate gradient algorithm with dynamic basis updating. (2020)
  6. Chen, Tyler; Carson, Erin: Predict-and-recompute conjugate gradient variants (2020)
  7. Terekhov, Kirill M.: Cell-centered finite-volume method for heterogeneous anisotropic poromechanics problem (2020)
  8. Terekhov, Kirill M.; Tchelepi, Hamdi A.: Cell-centered finite-volume method for elastic deformation of heterogeneous media with full-tensor properties (2020)
  9. Aihara, Kensuke; Komeyama, Ryosuke; Ishiwata, Emiko: Variants of residual smoothing with a small residual gap (2019)
  10. Maday, Yvon; Marcati, Carlo: Regularity and (hp) discontinuous Galerkin finite element approximation of linear elliptic eigenvalue problems with singular potentials (2019)
  11. Nair, Prapanch; Tomar, Gaurav: Simulations of gas-liquid compressible-incompressible systems using SPH (2019)
  12. Nguyen, Minh Tuan; Jeon, Byoung Jin; Chang, Hyuk-Jae; Lee, Sang-Wook: Domain decomposition based parallel computing for multi-scale coronary blood flow simulations (2019)
  13. Pei, Chaoxu; Vahab, Mehdi; Sussman, Mark; Hussaini, M. Yousuff: A hierarchical space-time spectral element and moment-of-fluid method for improved capturing of vortical structures in incompressible multi-phase/multi-material flows (2019)
  14. Abe, Kuniyoshi; Fujino, Seiji: Converting BiCR method for linear equations with complex symmetric matrices (2018)
  15. 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)
  16. Carson, Erin C.: The adaptive (s)-step conjugate gradient method (2018)
  17. 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)
  18. 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)
  19. Aihara, Kensuke: Variants of the groupwise update strategy for short-recurrence Krylov subspace methods (2017)
  20. Guérillot, Dominique; Bruyelle, Jérémie: Compositional dual mesh method for single phase flow in heterogeneous porous media -- application to CO(_2) storage (2017)

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