  Widely employed for the accurate solution of the electroencephalography
forward problem, the symmetric formulation gives rise to a first kind,
ill-conditioned operator ill-suited for complex modelling scenarios. This work
presents a novel preconditioning strategy based on an accurate spectral
analysis of the operators involved which, differently from other
Calder\'on-based approaches, does not necessitate the barycentric refinement of
the primal mesh (i.e., no dual matrix is required). The discretization of the
new formulation gives rise to a well-conditioned, symmetric, positive-definite
system matrix, which can be efficiently solved via fast iterative techniques.
Numerical results for both canonical and realistic head models validate the
effectiveness of the proposed formulation.
