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Hyperbolic Polynomial Toolbox (HPT)

version 1.0.0.0 (407 KB) by Zachary Harris
Tools for working with hyperbolic polynomials, especially matrix and tensor representations.

679 Downloads

Updated 30 Sep 2010

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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.

Cite As

Zachary Harris (2021). Hyperbolic Polynomial Toolbox (HPT) (https://www.mathworks.com/matlabcentral/fileexchange/28895-hyperbolic-polynomial-toolbox-hpt), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2008a
Compatible with any release
Platform Compatibility
Windows macOS Linux
Acknowledgements

Inspired by: perms

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