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 299 articles , 1 standard article )

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  1. 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)
  2. Itoh, Shoji; Sugihara, Masaaki: Changing over stopping criterion for stable solving nonsymmetric linear equations by preconditioned conjugate gradient squared method (2020)
  3. Li, Lidan; Zhang, Liwei; Zhang, Hongwei: Inverse semidefinite quadratic programming problem with (l_1) norm measure (2020)
  4. Aihara, Kensuke; Komeyama, Ryosuke; Ishiwata, Emiko: Variants of residual smoothing with a small residual gap (2019)
  5. 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)
  6. Nguyen, N. C.; Fernandez, P.; Freund, R. M.; Peraire, J.: Accelerated residual methods for the iterative solution of systems of equations (2018)
  7. 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)
  8. Vuik, C.: Krylov subspace solvers and preconditioners (2018)
  9. Aihara, Kensuke: Variants of the groupwise update strategy for short-recurrence Krylov subspace methods (2017)
  10. Dehghan, Mehdi; Mohammadi-Arani, Reza: Generalized product-type methods based on bi-conjugate gradient (GPBiCG) for solving shifted linear systems (2017)
  11. Gillis, T.; Winckelmans, G.; Chatelain, P.: An efficient iterative penalization method using recycled Krylov subspaces and its application to impulsively started flows (2017)
  12. Niemimäki, Ossi; Kurz, Stefan; Kettunen, Lauri: Structure-preserving mesh coupling based on the Buffa-Christiansen complex (2017)
  13. Suñé, Víctor; Carrasco, Juan Antonio: Implicit ODE solvers with good local error control for the transient analysis of Markov models (2017)
  14. Duintjer Tebbens, Jurjen; Meurant, Gérard: On the convergence of Q-OR and Q-MR Krylov methods for solving nonsymmetric linear systems (2016)
  15. Gu, Xian-Ming; Huang, Ting-Zhu; Carpentieri, Bruno: BiCGCR2: A new extension of conjugate residual method for solving non-Hermitian linear systems (2016)
  16. Hajarian, Masoud: Symmetric solutions of the coupled generalized Sylvester matrix equations via BCR algorithm (2016)
  17. Liu, Zhengguang; Li, Xiaoli: A parallel CGS block-centered finite difference method for a nonlinear time-fractional parabolic equation (2016)
  18. Rieutord, Michel; Espinosa Lara, Francisco; Putigny, Bertrand: An algorithm for computing the 2D structure of fast rotating stars (2016)
  19. Ahuja, Kapil; Benner, Peter; de Sturler, Eric; Feng, Lihong: Recycling BiCGSTAB with an application to parametric model order reduction (2015)
  20. 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)

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