Abstract
GPBiCG is a generalization of a class of product-type methods where the residual polynomials can be factored by the residual polynomial of BiCG and other polynomials with standard three-term recurrence relations. Actually this method generalizes CGS and BiCGStab methods. In this paper we use GPBiCG to present a new method for solving shifted linear systems. GPBiCG is faster than BiCGStab and its convergence is smoother than CGS. So here we are expecting to develop a method which is faster and its convergence is smoother than shifted BiCGStab and shifted CGS methods for solving shifted linear systems.
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The authors are very grateful to the two referees for their useful comments and suggestions that helped us improve the presentation of this paper.
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Communicated by Jinyun Yuan.
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Dehghan, M., Mohammadi-Arani, R. Generalized product-type methods based on bi-conjugate gradient (GPBiCG) for solving shifted linear systems. Comp. Appl. Math. 36, 1591–1606 (2017). https://doi.org/10.1007/s40314-016-0315-y
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DOI: https://doi.org/10.1007/s40314-016-0315-y
Keywords
- Shifted linear systems
- Krylov methods
- Shifted GPBiCG
- Shifted BiCGStab
- Shifted conjugate-gradient squared (CGS)
- Quantum chrmodynamics