  Block and global Krylov subspace methods have been proposed as methods
adapted to the situation where one iteratively solves systems with the same
matrix and several right hand sides. These methods are advantageous, since they
allow to cast the major part of the arithmetic in terms of matrix-block vector
products, and since, in the block case, they take their iterates from a
potentially richer subspace. In this paper we consider the most established
Krylov subspace methods which rely on short recurrencies, i.e. BiCG, QMR and
BiCGStab. We propose modifications of their block variants which increase
numerical stability, thus at least partly curing a problem previously observed
by several authors. Moreover, we develop modifications of the "global" variants
which almost halve the number of matrix-vector multiplications. We present a
discussion as well as numerical evidence which both indicate that the
additional work present in the block methods can be substantial, and that the
new "economic" versions of the "global" BiCG and QMR method can be considered
as good alternatives to the BiCGStab variants.
