To analyze polydisperse systems of nanoparticles, the particle size distribution function can be determined from small-angle X-ray and neutron scattering data using some algorithms. The corresponding least squares problem is an ill-posed problem; correspondingly, a solution can strongly depend on the initial approximation and the parameters of search algorithms. A procedure based on solving a system of linear equations with regularization gives a stable solution, but it is not free of artifacts. Other algorithms that seek the distribution function both in an analytical form and in the form of a nonparametric histogram provide solutions that can depend on the search parameters and the initial approximation. In this work, a combined scheme of using these algorithms has been proposed to increase the stability of the solution and, thereby, its reliability.

为了分析纳米粒子的多分散系统，可以使用一些算法从小角度X射线和中子散射数据确定粒度分布函数。相应的最小二乘问题是不适定问题；相应地，解决方案可能在很大程度上取决于初始近似和搜索算法的参数。基于带正则化的线性方程组系统求解的过程给出了稳定的解决方案，但并非没有伪影。寻求解析形式和非参数直方图形式的分布函数的其他算法提供的解决方案可能取决于搜索参数和初始近似值。在这项工作中，已经提出了使用这些算法的组合方案，以提高解决方案的稳定性，从而，