A graphical tool for driving the parallel computation of pseudosprectra

• Authors: Dany Mezher
• Venue: ICS '01 Proceedings of the 15th international conference on Supercomputing
• Year: 2001

This paper presents the programming environment of a new tool for the parallel computation of Pseudospectra. Based on the PPA Talgorithm described in [16, 17], this algorithm offers total reliability and can handle singularities along the level curve without difficulty. It offers a guarantee of termination even in the presence of round-off errors and makes use of the large granularity for parallelism in PAT [17]. This results in large speedups and high efficiency. The software is able to trace multiple level curves simultaneously and task in to account the symmetry of the pseudospectrum in the case of real matrices to reduce the total computational cost. The ability of the software to compute multiple slices of the same level curve simultaneously enhances the speedup and efficiency. The user drives the parallel application through a graphical user interface. The interface includes graphical features (zoom in, zoom out, color control,…) and computational features (raise or lower level curve priority, limit computation to a set of processors,…) crucial for the appreciation of the information provided by the pseudospectrum. Although the application was developed for the computation of the pseudospectrum, it can be used, provided minor modifications, to trace the level curves of any continuous, not necessarily smooth, function f(z): C → R