CONKUB: A conversational path-follower for systems of nonlinear equations
Journal of Computational Physics
A new algorithm for numerical path following applied to an example from hydrodynamical flow
SIAM Journal on Scientific and Statistical Computing
Task scheduling for parallel sparse Cholesky factorization
International Journal of Parallel Programming
Parallel algorithms for sparse linear systems
SIAM Review
Parallel sparse QR factorization on shared memory architectures
Parallel Computing
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
Computation of Pseudospectra by Continuation
SIAM Journal on Scientific Computing
A Fast Implementation of the Minimum Degree Algorithm Using Quotient Graphs
ACM Transactions on Mathematical Software (TOMS)
A graphical tool for driving the parallel computation of pseudosprectra
ICS '01 Proceedings of the 15th international conference on Supercomputing
Numerical Computation, Volume I
Numerical Computation, Volume I
Parallel Computation of Spectral Portraits on the Meiko CS2
HPCN Europe 1996 Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking
A graphical tool for driving the parallel computation of pseudosprectra
ICS '01 Proceedings of the 15th international conference on Supercomputing
Parallel Computation of Pseudospectra Using Transfer Functions on a MATLAB-MPI Cluster Platform
Proceedings of the 9th European PVM/MPI Users' Group Meeting on Recent Advances in Parallel Virtual Machine and Message Passing Interface
Computing smallest singular triplets with implicitly restarted Lanczos bidiagonalization
Applied Numerical Mathematics - Numerical algorithms, parallelism and applications
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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.