The aim of the master thesis is to apply the Hermitian and skew-Hermitian (HSS)
iterative method and its inexact version to the solution of linear algebraic systems,
arising in different applications, with symmetric, but indefinite system matrices.
In particular, we consider saddle-point problems coming from a reformulation of the well-known
domain decomposition Finite Element Tearing and Interconnecting method as a saddle-point
problem with both primal and dual variables as unknowns. This is an alternative,
hopefully better, approach to the existing methods, namely block-structured preconditioners
combined with suitable Krylov subspace methods or Schur-complement conjugate gradient methods.
The convergence of HSS method is studied numerically. The numerical experiments show that the
use of the HSS method as a preconditioner in a Krylov subspace method is very efficient.
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