Generalized product-type methods based on bi-conjugate gradient (GPBiCG) for solving shifted linear systems. (English) Zbl 1383.65025

Summary: 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 conjugate-gradient squared (CGS) and bi-conjugate-gradient stabilized (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.


65F10 Iterative numerical methods for linear systems
81V05 Strong interaction, including quantum chromodynamics
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