BiCGStab(l) for families of shifted linear systems

We consider a seed system Ax = b together with a shifted linear system of the form (A + sigmaI)x = b, sigma is an element of C, A is an element of C-nxn, b is an element of C-n. We develop modifications of the BiCGStab(l) method which allow to solve the seed and the shifted system at the expense of just the matrix-vector multiplications needed to solve Ax = b via BiCGStab(l). On the shifted system, these modifications do not perform the corresponding BiCGStab(l)-method, but we show, that in the case that A is positive real and sigma > 0, the resulting method is still a well-smoothed variant of BiCG. Numerical examples from an application arising in quantum chromodynamics are given to illustrate the efficiency of the method developed.