Curve fitting and identification of physical spectra (Q1919511)

The identification of peak superpositions and the determination of the single-peak intensities are studied on the model function \[ \eta(a, x, t):= \sum^q_{i= 1} a_i \exp\Biggl(- {(t- x_i)^2\over 2x^2_{i+ q}}\Biggr)+ a_{q+ 1} t^2+ a_{q+ 2} t+ a_{q+ 3}. \] The composition of the parameters \(a_i\), \(a_{q+ i}\), and \(x_i\) in the model function is evaluated. A modification of the trust-region Gauss-Newton method for the solution of separable nonlinear least squares problem is used (with a two-parameter approximation). The method of regularized variable projection is described to find an algorithm (its 7 steps are given) for the approximation. An application of the method for the identification of spectra of X-ray emission analyses (Ta, Mo, Ga phosphide, chromium manganese, and 3 other analyses) is studied.