Method of singular value decomposition at the problem of determining the chemical composition of a medium

摘要

The problem of finding the chemical composition of a homogeneousmedium by the method of multi-energy radiography is considered.The main attention is paid to the choice of optimal energy values of Xrayradiation and to derivation of accurate estimates of the perturbationof the solution of the system of equations for given perturbations ofthe right-hand side. For this purpose the method of Singular ValueDecomposition of the matrix was used. Singular numbers and singularvectors corresponding to a number of groups of chemical elements, oftenencountered in practice, are calculated. Optimum values of X-ray radiationenergy for these groups of elements are found. The results obtainedhas been compared with the case of overdetermined system solution.Several examples of the solution of the problem for media of differentchemical composition have been constructed.