We have previously investigated a method of high-energy x-ray spectral reconstruction from transmission data by direct resolution of a matrix system. This technique uses the spectral vectorial algebra formalism. The resolution has previously been tested on a 12 MV photon beam. To extend and to test the validity of the results to the entire radiotherapy energy range, we have performed the method on photon beams with nominal energies of 6, 12, 15, and 25 MV. The influence on the 6 MV spectrum of a 60 degrees built-in wedge has also been investigated to test the sensitivity of the method and the results are reported. To validate our reconstructed spectra, dosimetric quantities such as tissue phantom ratios (TPR), water-to-air stopping power ratios (S/rho)(air)(water), and quality indexes TPR1020 have been calculated. The results show good agreement between the measured and calculata data. Mean mass energy absorption coefficient ratios for different materials have also been computed and compared to data published recently and the results are very close (within +/-0.5%). Primary depth dose functions in water have also been computed to deduce primary dose attenuation coefficients. (C) 1997 American Association of Physicists in Medicine.