  An inverse problem in spectroscopy is considered. The objective is to restore
the discrete spectrum from observed spectrum data, taking into account the
spectrometer's line spread function. The problem is reduced to solution of a
system of linear-nonlinear equations (SLNE) with respect to intensities and
frequencies of the discrete spectral lines. The SLNE is linear with respect to
lines' intensities and nonlinear with respect to the lines' frequencies. The
integral approximation algorithm is proposed for the solution of this SLNE. The
algorithm combines solution of linear integral equations with solution of a
system of linear algebraic equations and avoids nonlinear equations. Numerical
examples of the application of the technique, both to synthetic and
experimental spectra, demonstrate the efficacy of the proposed approach in
enabling an effective enhancement of the spectrometer's resolution.
