## Section: Software

### PPAT: pseudo-spectrum

Participants : Édouard Canot [corresponding author] , Bernard Philippe.

PPAT (Parallel PATh following software) is a parallel code, developed by D. Mezher, W. Najem (University of Saint-Joseph, Beirut, Lebanon) and B. Philippe. This tool can follow the contours of a functional from $\u2102$ to ${\mathbb{R}}^{+}$. The present version is adapted for determining the level curves of the function $f\left(z\right)={\sigma}_{min}(A-zI)$ which gives the pseudospectrum of matrix $A$.

The algorithm is reliable: it does not assume that the curve has a derivative everywhere. The process is proved to terminate even when taking into account roundoff errors. The structure of the code spawns many independent tasks which provide a good efficiency in the parallel runs.

The software can be downloaded under the GPL licence from: http://sourceforge.net/projects/ppat .