  Sylvester matrix equations are ubiquitous in scientific computing. However,
few solution techniques exist for their generalized multiterm version, as they
now arise in an increasingly large number of applications. In this work, we
consider algebraic parameter-free preconditioning techniques for the iterative
solution of generalized multiterm Sylvester equations. They consist in
constructing low Kronecker rank approximations of either the operator itself or
its inverse. While the former requires solving standard Sylvester equations in
each iteration, the latter only requires matrix-matrix multiplications, which
are highly optimized on modern computer architectures. Moreover, low Kronecker
rank approximate inverses can be easily combined with sparse approximate
inverse techniques, thereby enhancing their performance with little or no
damage to their effectiveness.
