Computing tall skinny solutions of AX−XB=C Original Research Article

We will concentrate on the numerical computation of so-called tall and skinny solutions X of the Sylvester equations AX−XB=C. By this we mean that A is an n×n matrix with cheaply applicable action (A is for example sparse), and B a k×k matrix, with k≪n. This type of Sylvester equation plays an important role in the computation of invariant subspaces when block Rayleigh quotient or block Jacobi–Davidson methods are used.