# Univariate Gaussian Splitting

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!

• The online documentation has tutorials on optimization. Just type in "optimization" (without the quotes) in the Wolfram Documentation search box. You should also lookup "WorkingPrecision" and "ControllingThePrecisionOfResults". Finally, don't be surprised if this question is closed because it is too broad and does not have evidence of what you've tried in Mathematica. But please don't let that deter you from asking questions in this forum. – JimB Oct 9 at 14:29