A new iterative method which is a hybrid of the BiCGSTAB and GPBiCG methods is proposed. The present method is an extension of the BiCGSTAB2 method. In the BiCGSTAB2 method which is a hybrid type method, two parameters of the BiCGSTAB method are adopted at even iteration step, and those of the GPBiCG method are used at odd iteration step. In the present GPBiCG(m,ℓ) method, parameters of the BiCGSTAB method are adopted at consecutive m iteration steps, and afterwards those of the GPBiCG method are also utilized in succession at ℓ iteration steps. We will examine the convergence property of the GPBiCG(m,ℓ) method and investigate its effectiveness through numerical experiments.

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  1. Dehghan, Mehdi; Mohammadi-Arani, Reza: Generalized product-type methods based on bi-conjugate gradient (GPBiCG) for solving shifted linear systems (2017)
  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. Peter, S.; De, A. K.: A parallel implementation of the ghost-cell immersed boundary method with application to stationary and moving boundary problems (2016)
  4. Zhang, Jianhua; Dai, Hua: Global GPBiCG method for complex non-Hermitian linear systems with multiple right-hand sides (2016)
  5. Zuo, Xian-Yu; Zhang, Li-Tao; Gu, Tong-Xiang; Zheng, Feng-Bin; Li, Ning: A parallel version of GPBi-CG method suitable for distributed parallel computing (2016)
  6. Ahuja, Kapil; Benner, Peter; de Sturler, Eric; Feng, Lihong: Recycling BiCGSTAB with an application to parametric model order reduction (2015)
  7. Su, Lijiong; Imakura, Akira; Tadano, Hiroto; Sakurai, Tetsuya: Improving the convergence behaviour of BiCGSTAB by applying (D)-norm minimization (2015)
  8. Xie, Ya-Jun; Ma, Chang-Feng: The MGPBiCG method for solving the generalized coupled Sylvester-conjugate matrix equations (2015)
  9. Zhang, Jianhua; Dai, Hua: A transpose-free quasi-minimal residual variant of the CORS method for solving non-Hermitian linear systems (2015)
  10. Zhang, Jianhua; Dai, Hua: A new quasi-minimal residual method based on a biconjugate (A)-orthonormalization procedure and coupled two-term recurrences (2015)
  11. De, A. K.: An implicit non-staggered Cartesian grid method for incompressible viscous flows in complex geometries (2014)
  12. Sun, Dong-Lin; Jing, Yan-Fei; Huang, Ting-Zhu; Carpentieri, Bruno: A quasi-minimal residual variant of the BiCORSTAB method for nonsymmetric linear systems (2014)
  13. Yeung, Man-Chung: ML((n))BiCGStabt: a ML((n))BiCGStab variant with (\mathbfA)-transpose (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. de Araújo, F. C.; D’Azevedo, E. F.; Gray, L. J.; Degenhardt, R.: A SBS-BD based solver for domain decomposition in BE methods (2013)
  17. Rendel, Olaf; Rizvanolli, Anisa; Zemke, Jens-Peter M.: IDR: a new generation of Krylov subspace methods? (2013)
  18. Suito, Hiroshi; Ueda, Takuya; Sze, Daniel: Numerical simulation of blood flow in the thoracic aorta using a centerline-fitted finite difference approach (2013)
  19. Zhao, Liang; Huang, Ting-Zhu; Jing, Yan-Fei; Deng, Liang-Jian: A generalized product-type BiCOR method and its application in signal deconvolution (2013)
  20. Abe, Kuniyoshi; Sleijpen, Gerard L. G.: Hybrid Bi-CG methods with a Bi-CG formulation closer to the IDR approach (2012)

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