Some preconditioning techniques for a class of double saddle point problems
Fariba Balani Bakrani, Luca Bergamaschi, Ángeles Martínez, Masoud Hajarian
Abstract
Summary In this paper, we describe and analyze the spectral properties of several 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 (F)GMRES method. We develop a spectral analysis of the preconditioned matrix showing that the complex eigenvalues lie in a circle of center 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.