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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