  The tangent plane scheme is a time-marching scheme for the numerical solution
of the nonlinear parabolic Landau-Lifshitz-Gilbert equation (LLG), which
describes the time evolution of ferromagnetic configurations. Exploiting the
geometric structure of LLG, the tangent plane scheme requires only the solution
of one linear variational form per time-step, which is posed in the discrete
tangent space determined by the nodal values of the current magnetization. We
develop an effective solution strategy for the arising constrained linear
systems, which is based on appropriate Householder reflections. We derive
possible preconditioners, which are (essentially) independent of the time-step,
and prove that the preconditioned GMRES algorithm leads to linear convergence.
Numerical experiments underpin the theoretical findings.
