Determinantal matrix representations of hyperbolic polynomials are a current topic of interest and research among those working with LMI's (Linear Matrix Inequalities) and SDP (semi-definite programming). This toolbox was used to demonstrate some of the theorems presented in the author's Ph.D. dissertation, "Abstract and Real Matrix Representations of Hyperbolic Polynomials", National University of Singapore, 2009. A copy of the dissertation is included in the root directory of the toolbox.
In particular, given a real hyperbolic polynomial p in direction e, we can effectively produce a linearly parametrized (in x) non-symmetric matrix representation M(x) which has eigenvalues which precisely line up with the eigenvalues of p and its higher order derivatives. Thus x is in the open hyperbolicity cone K(p;e) if and only if M(x) has all positive eigenvalues.
See the README file for a brief introduction to HPT. Example of how to run HPT can be found in the setup.m script and in the appendix to the dissertation.
Zachary Harris (2022). Hyperbolic Polynomial Toolbox (HPT) (https://www.mathworks.com/matlabcentral/fileexchange/28895-hyperbolic-polynomial-toolbox-hpt), MATLAB Central File Exchange. Retrieved .
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