Before revision:  In this note we analyze in detail how the EIM at each iteration attempts to choose the interpolation nodes so as to make the related Vandermonde-type matrix " as invertible as possible " as well as attempting to optimize the conditioning of its inversion and minimizing a Lebesgue-type constantfor accuracy.
After revision:  In this note we analyze in detail how the EIM at each iteration chooses the interpolation nodes so as to make the related Vandermonde-type matrix " as invertible as possible " as well as attempting to optimize the conditioning of its inversion and minimizing a Lebesgue-type constantfor accuracy.