Gradient descent approach for the hausdorff problem

This work considers the Hausdorff moment problem and proposes a gradient descent approach as a tool to solve the linear system generated from the spline or B-spline construction. In fact, the linear system that is built from the given moments is ill-conditioned. But, with the gradient descent, the more order moment available, the more efficient minimization is obtained. Additionally, since the reconstruction should approximate a distribution, its values should be non-negative. The projected gradient descent controls the positivity of the solution. Our method is tested on different types of functions confirming the fact that using more moments reduces the efficiency of the standard linear algebra solutions, while the gradient descent minimization becomes more efficient.