  In this paper, we describe and analyze the spectral properties of a number of
exact block preconditioners for a class of double saddle point problems. Among
all these, we consider an inexact version of a block triangular preconditioner
providing extremely fast convergence of the FGMRES method. We develop a
spectral analysis of the preconditioned matrix showing that the complex
eigenvalues lie in a circle of center (1,0) and radius 1, while the real
eigenvalues are described in terms of the roots of a third order polynomial
with real coefficients. Numerical examples are reported to illustrate the
efficiency of inexact versions of the proposed preconditioners, and to verify
the theoretical bounds.
