Parallel computation of pseudospectra of large sparse matrices

The parallel computation of the pseudospectrum is presented. The Parallel Path following Algorithm using Triangles (PPAT) is based on the Path following Algorithm using Triangles (PAT). This algorithm offers total reliability and can handle singular points along the level curve without difficulty. Furthermore, PPAT offers a guarantee of termination even in the presence of round-off errors and makes use of the large granularity for parallelism in PAT. This results in large speedups and high efficiency. The PPAT is able to trace multiple level curves simultaneously and takes into account the symmetry of the pseudospectrum in the case of real matrices to reduce the total computational cost.