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. Gu, Xian-Ming; Huang, Ting-Zhu; Carpentieri, Bruno: BiCGCR2: A new extension of conjugate residual method for solving non-Hermitian linear systems (2016)
  2. Zhang, Jianhua; Dai, Hua: Global GPBiCG method for complex non-Hermitian linear systems with multiple right-hand sides (2016)
  3. Ahuja, Kapil; Benner, Peter; de Sturler, Eric; Feng, Lihong: Recycling BiCGSTAB with an application to parametric model order reduction (2015)
  4. Zhang, Jianhua; Dai, Hua: A new quasi-minimal residual method based on a biconjugate $A$-orthonormalization procedure and coupled two-term recurrences (2015)
  5. Zhang, Jianhua; Dai, Hua: A transpose-free quasi-minimal residual variant of the CORS method for solving non-Hermitian linear systems (2015)
  6. De, A.K.: An implicit non-staggered Cartesian grid method for incompressible viscous flows in complex geometries (2014)
  7. Yeung, Man-Chung: ML($n$)BiCGStabt: a ML($n$)BiCGStab variant with $\bold A$-transpose (2014)
  8. Zhu, Sheng-Xin; Gu, Tong-Xiang; Liu, Xing-Ping: Minimizing synchronizations in sparse iterative solvers for distributed supercomputers (2014)
  9. Abe, Kuniyoshi; Sleijpen, Gerard L.G.: Solving linear equations with a stabilized GPBiCG method (2013)
  10. 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)
  11. Rendel, Olaf; Rizvanolli, Anisa; Zemke, Jens-Peter M.: IDR: a new generation of Krylov subspace methods? (2013)
  12. Suito, Hiroshi; Ueda, Takuya; Sze, Daniel: Numerical simulation of blood flow in the thoracic aorta using a centerline-fitted finite difference approach (2013)
  13. Zhao, Liang; Huang, Ting-Zhu; Jing, Yan-Fei; Deng, Liang-Jian: A generalized product-type BiCOR method and its application in signal deconvolution (2013)
  14. Abe, Kuniyoshi; Sleijpen, Gerard L.G.: Hybrid Bi-CG methods with a Bi-CG formulation closer to the IDR approach (2012)
  15. Imakura, Akira; Sogabe, Tomohiro; Zhang, Shao-Liang: An efficient variant of the GMRES($m$) method based on the error equations. (2012)
  16. Du, Lei; Sogabe, Tomohiro; Zhang, Shao-Liang: A variant of the IDR$(s)$ method with the quasi-minimal residual strategy (2011)
  17. Kanayama, Hiroshi; Tsukikawa, Hisayoshi: Simulation of hydrogen dispersion by the domain decomposition method (2011)
  18. Nagaoka, Shinsuke; Nakabayashi, Yasushi; Yagawa, Genki; Kim, Young Jin: Accurate fluid-structure interaction computations using elements without mid-side nodes (2011)
  19. Abe, Kuniyoshi; Sleijpen, Gerard L.G.: BiCR variants of the hybrid BiCG methods for solving linear systems with nonsymmetric matrices (2010)
  20. Tanio, Masaaki; Sugihara, Masaaki: GBi-CGSTAB($s,L$): IDR($s$) with higher-order stabilization polynomials (2010)

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