A novel trilinear direct decomposition algorithm is proposed for the decomposi-tion of a three-dimensional matrix consisting of several samples of measured two-dimensional data. The abstract spectral and concentration matrices are obtained by high-dimensional principal component analysis. Then the unique solutions of spectra and concentrations of the components are determined by the QZ algorithm. The new method is robust in noise environment and suitable for qualitative and quantitative analysis of high-dimensional... A novel trilinear direct decomposition algorithm is proposed for the decomposi-tion of a three-dimensional matrix consisting of several samples of measured two-dimensional data. The abstract spectral and concentration matrices are obtained by high-dimensional principal component analysis. Then the unique solutions of spectra and concentrations of the components are determined by the QZ algorithm. The new method is robust in noise environment and suitable for qualitative and quantitative analysis of high-dimensional grey system and multi-point calibration. The simulated data were used for exploring the effect of spectral resolution to the precision of prediction. In fluorescence analysis of mixtures of vitamin B1, vitamin B2 and vitamin B6, the results show that the obtained spectra and concentrations are in agreement with the experimental values. |