If you're looking for a neat convergence analysis comparable to the ones of GMRES/MINRES type methods then there is none. At least none that i'm aware of.

However, for QMR there are some results that relate the QMR residuals in some sense to the GMRES residuals (see the original QMR papers).

Thank you, Patrick. I knew the residual relation between QMR and GMRES. However, as u said, there seems to be no neat convergence analysis of BiCG-type methods in the literature. Maybe it's still an open problem.

Hello again, Ke Zhang! I have demonstrated in my papers that the use of BiCGStab or BiCGStab(2) may be a very good alternative for solution of large and sparse linear systems. Furthermore, the parallelization of such methods is a better solution to run on the NVidia's GPUs.

@Lauro de Paula: Thanks for your suggestion. I will have a look at your paper.

Hello, Ke Zhang! Thank you for making yourself available in order to read my paper.