Polynomial (chaos) approximation of the maximum eigenvalue functions: efficiency and limitations

Further analysis and matlab codes are available for polynomial (chaos) approximation of the uncertain delay differential euqations stability measure

The recent developments explicit the parallelism between polynomial chaos theory and polynomial approximation, reviewing the convergence results of this latter framework.

Article: L. Fenzi & W. Michiels, Polynomial (chaos) approximation of maximum eigenvalue functions: efficiency and limitations, Numerical Algorithms https://doi.org/10.1007/s11075-018-00648-9 (2019).

Matlab Tutorial: L. Fenzi & W. Michiels, Experiments on polynomial (chaos) approximation of maximum eigenvalue functions: Tutorial Technical Report KU Leuven, Department of Computer Science http://www.cs.kuleuven.be/publicaties/rapporten/tw/TW688.abs.html (2018).

Polynomial Chaos Theory: Application to the stability of Uncertain Delay Differential Equations

Matlab codes

In this repository, all the Matlab codes, used for developing my Master Thesis: "Polynomial Chaos Theory: Application to the stability of Uncertain Delay Differential Equations", are collected. The thesis furnishes all the theoretical bases and the motivations for implementing the codes that you find in these folders. Moreover, the notation used to develop the code is taken by the thesis.

If you do not possess the Thesis and you want to see it please send an email to fenzi.luca@gmail.com. I am very glad to share this document with the interested people.

For simplicity, the codes are divided in folders following the chapter of the thesis:

1. Basic Concepts of Probability Theory 2ch_Probability

2. Orthogonal Polynomials and Approximation Theory 3ch_Approximation

3. Polynomial Chaos Theory 4ch_PCE

4. Uncertain Delay Differential Equation 5ch_UDDE

5. Computational Results 6ch_Results

In every folder, you find another README file with a short explanation of the codes of the folder. In this folder, you can find only the Hard Cover of the thesis.

The codes are implemented in MATLAB r2015a, and they are extensively used to develop all the figures and the tables of my thesis. In particular, the figures and the tables were inserted in tex using the Matlab function matlab2tikz and matrix2latex.

All the attendants are kindly invited and encouraged to report on possible (and inevitable) mistakes and improvements of the present codes. I appreciate every contribution and collaboration; feel free to write me.

Luca Fenzi

fenzi.luca@gmail.com