We present in this paper an application of the Lanczos algorithm to the fitting of a potential energy surface from the experimental spectrum. This method presents two definite improvements on the conventional approach: (i) the Lanczos algorithm allows to treat ultra-large basis sets (120 000 states in this calculation) and (ii) it is possible to tune selectively the calculation to specific components of the spectrum (e.g., a given combination band nνi+mνj) thus reducing considerably the complexity of the fit. This method has been applied to the CD3H molecule, considering all the vibrational degrees of freedom. Converged line positions have been obtained for high overtones of the C-H stretching mode (up to 16 000 cm-1). The accuracy of the fitted surface is demonstrated by direct comparison of experimental and calculated spectroscopical parameters.