CGS, a fast Lanczos-type solver for nonsymmetric linear systems The presented method is a combination of the CGS algorithm (a “squared” conjugate gradient method) with a preconditioning called ILLU (an incomplete line-LU-factorization). The conclusion of the author is that this combination is a competitive solver for nonsymmetric linear systems, at least for problems that are not too large, and when high accuracy is required. Numerical experiments show that the average work for solving convection-diffusion equations in two dimensions is roughly O(N 3/2 ).

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 308 articles , 1 standard article )

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  1. Maia, A. A. G.; Cavalca, D. F.; Tomita, J. T.; Costa, F. P.; Bringhenti, C.: Evaluation of an effective and robust implicit time-integration numerical scheme for Navier-Stokes equations in a CFD solver for compressible flows (2022)
  2. Jia, ZhiGang; Ng, Michael K.: Structure preserving quaternion generalized minimal residual method (2021)
  3. Taherian, A.; Toutounian, F.: Block GPBi-CG method for solving nonsymmetric linear systems with multiple right-hand sides and its convergence analysis (2021)
  4. Cao, Rongjun; Chen, Minghua; Ng, Michael K.; Wu, Yu-Jiang: Fast and high-order accuracy numerical methods for time-dependent nonlocal problems in (\mathbbR^2) (2020)
  5. El Madkouri, Abdessamad; Ellabib, Abdellatif: A preconditioned Krylov subspace iterative methods for inverse source problem by virtue of a regularizing LM-DRBEM (2020)
  6. Itoh, Shoji; Sugihara, Masaaki: Changing over stopping criterion for stable solving nonsymmetric linear equations by preconditioned conjugate gradient squared method (2020)
  7. Li, Lidan; Zhang, Hongwei; Zhang, Liwei: Inverse quadratic programming problem with (l_1) norm measure (2020)
  8. Li, Lidan; Zhang, Liwei; Zhang, Hongwei: Inverse semidefinite quadratic programming problem with (l_1) norm measure (2020)
  9. Montoison, Alexis; Orban, Dominique: BiLQ: an iterative method for nonsymmetric linear systems with a quasi-minimum error property (2020)
  10. Saad, Yousef: Iterative methods for linear systems of equations: a brief historical journey (2020)
  11. Aihara, Kensuke; Komeyama, Ryosuke; Ishiwata, Emiko: Variants of residual smoothing with a small residual gap (2019)
  12. de Araujo, Francisco C.; Hillesheim, Maicon J.; Soares, Delfim: Revisiting the BE SBS algorithm and applying it to solve torsion problems in composite bars: robustness and efficiency study (2019)
  13. Nguyen, N. C.; Fernandez, P.; Freund, R. M.; Peraire, J.: Accelerated residual methods for the iterative solution of systems of equations (2018)
  14. Tůma, Karel; Stein, Judith; Průša, Vít; Friedmann, Elfriede: Motion of the vitreous humour in a deforming eye-fluid-structure interaction between a nonlinear elastic solid and viscoelastic fluid (2018)
  15. Vuik, C.: Krylov subspace solvers and preconditioners (2018)
  16. Aihara, Kensuke: Variants of the groupwise update strategy for short-recurrence Krylov subspace methods (2017)
  17. Dehghan, Mehdi; Mohammadi-Arani, Reza: Generalized product-type methods based on bi-conjugate gradient (GPBiCG) for solving shifted linear systems (2017)
  18. Gillis, T.; Winckelmans, G.; Chatelain, P.: An efficient iterative penalization method using recycled Krylov subspaces and its application to impulsively started flows (2017)
  19. Niemimäki, Ossi; Kurz, Stefan; Kettunen, Lauri: Structure-preserving mesh coupling based on the Buffa-Christiansen complex (2017)
  20. Suñé, Víctor; Carrasco, Juan Antonio: Implicit ODE solvers with good local error control for the transient analysis of Markov models (2017)

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