This paper proposes a new method for the inverse problem of the three-dimensional
reconstruction of the electrical activity of the brain from electroencephalography (EEG). Compared
to conventional direct methods using additional parameters, the proposed approach solves
the EEG inverse problem iteratively without any parameter. We describe the Lagrangian corresponding
to the minimization problem and suggest the numerical inverse algorithm. The
restriction of influence space and the lead field matrix reduce the computational cost in this approach.
The reconstructed divergence of primary current converges to a reasonable distribution
for three dimensional sphere head model.