CGS

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 264 articles , 1 standard article )

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  1. Duintjer Tebbens, Jurjen; Meurant, Gérard: On the convergence of Q-OR and Q-MR Krylov methods for solving nonsymmetric linear systems (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. Ahuja, Kapil; Benner, Peter; de Sturler, Eric; Feng, Lihong: Recycling BiCGSTAB with an application to parametric model order reduction (2015)
  4. 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)
  5. Karageorghis, Andreas: The method of fundamental solutions for elliptic problems in circular domains with mixed boundary conditions (2015)
  6. Zhang, Li-Tao; Dong, Xiao-Na; Gu, Tong-Xiang; Zuo, Xian-Yu; Liu, Xing-Ping: An improved generalized conjugate residual squared (IGCRS2) algorithm suitable for distributed parallel computing (2015)
  7. Zhang, Li-Tao; Zuo, Xian-Yu; Gu, Tong-Xiang; Liu, Xing-Ping: A parallel generalized global conjugate gradient squared algorithm for linear systems with multiple right-hand sides (2015)
  8. Aihara, Kensuke; Abe, Kuniyoshi; Ishiwata, Emiko: A quasi-minimal residual variant of IDRstab using the residual smoothing technique (2014)
  9. Hajarian, Masoud: Matrix form of the CGS method for solving general coupled matrix equations (2014)
  10. Yeung, Man-Chung: ML($n$)BiCGStabt: a ML($n$)BiCGStab variant with $\bold A$-transpose (2014)
  11. Hajarian, Masoud: Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations (2013)
  12. Pestana, Jennifer; Wathen, Andrew J.: On the choice of preconditioner for minimum residual methods for non-Hermitian matrices (2013)
  13. Rendel, Olaf; Rizvanolli, Anisa; Zemke, Jens-Peter M.: IDR: a new generation of Krylov subspace methods? (2013)
  14. Zhao, Liang; Huang, Ting-Zhu; Jing, Yan-Fei; Deng, Liang-Jian: A generalized product-type BiCOR method and its application in signal deconvolution (2013)
  15. Zlatev, Zahari; Georgiev, Krassimir: Applying approximate LU-factorizations as preconditioners in eight iterative methods for solving systems of linear algebraic equations (2013)
  16. Abe, Kuniyoshi; Sleijpen, Gerard L.G.: Hybrid Bi-CG methods with a Bi-CG formulation closer to the IDR approach (2012)
  17. Ahuja, Kapil; De Sturler, Eric; Gugercin, Serkan; Chang, Eun R.: Recycling BICG with an application to model reduction (2012)
  18. Bai, Zheng-Jian; Serra-Capizzano, Stefano; Zhao, Zhi: Nonnegative inverse eigenvalue problems with partial eigendata (2012)
  19. Ferronato, Massimiliano: Preconditioning for sparse linear systems at the dawn of the 21st century: history, current developments, and future perspectives (2012)
  20. Amparore, E.G.; Donatelli, S.: Revisiting the matrix-free solution of Markov regenerative processes. (2011)

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