  Global and block Krylov subspace methods are efficient iterative solvers for
large sparse linear systems with multiple right-hand sides. However, global or
block Lanczos-type solvers often exhibit large oscillations in the residual
norms and may have a large residual gap relating to the loss of attainable
accuracy of the approximations. Conventional residual smoothing schemes
suppress these oscillations but cannot improve the attainable accuracy, whereas
a recent residual smoothing scheme enables the improvement of the attainable
accuracy for single right-hand side Lanczos-type solvers. The underlying
concept of this scheme is that the primary and smoothed sequences of the
approximations and residuals influence one another, thereby avoiding the severe
propagation of rounding errors. In the present study, we extend this
cross-interactive residual smoothing to the case of solving linear systems with
multiple right-hand sides. The resulting smoothed methods can reduce the
residual gap with a low additional cost compared to their original
counterparts. We demonstrate the effectiveness of the proposed approach through
rounding error analysis and numerical experiments.
