## 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.

### MSC:

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

### Software:

GpBiCg; MatrixMarket; CGS
Full Text:

### References:

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