I would like to experiment a bit with univariate Gaussian Split libraries.
This is essentially a constrained non-linear optimization (minimization) problem. There are multiple formulations of this problem. One is given in this paper (eq. 4 with constraints given in eqs. 5 and 6): http://www.techscience.com/doi/10.3970/cmes.2016.111.083.pdf
The results of this problem are also published in the paper and I would like to re-obtain them with Mathematica and play around a bit with the parameters involved in the problem.
Another formulation of the problem (different cost optimization metric) is given in this publication (equation 17): https://www.researchgate.net/publication/256158406_Entropy-Based_Approach_for_Uncertainty_Propagation_of_Nonlinear_Dynamical_Systems
The constraints for the first paper also apply to the second.
In the first paper it is written that quadruple precision might be needed for high numbers of N. I am still a Mathematica beginner, however I have the feeling that the software has great potential to help in this task. The following questions therefore arise:
1) Using features up to Mathematica 11.3, how can I formulate/solve the optimization problems found in the literature and play around a bit with the parameters?
1.5) Short side-task: An easy way to visualize the resulting splits would also be great!
2) Is Mathematica capable of the task, i.e. is quadruple precision supported/required? If not, is there any other software package available which quickly allows me to play around a bit without having to code the entire optimization procedure in quadruple precision in Fortran, as suggested in the first paper?
I read a bit about Mathematica's Minimize and NMinimize, however I did not succeed at all in formulating the vectorized description of the problem and was hoping to receive some help here.
Thanks to anyone spending time on this!