Calculation of pseudospectra by the Arnoldi iteration
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Pseudospectra of Linear Operators
SIAM Review
Restarted GMRES for Shifted Linear Systems
SIAM Journal on Scientific Computing
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Towards the effective parallel computation of matrix pseudospectra
ICS '01 Proceedings of the 15th international conference on Supercomputing
MultiMATLAB: integrating MATLAB with high-performance parallel computing
SC '97 Proceedings of the 1997 ACM/IEEE conference on Supercomputing
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
Large-Scale Computation of Pseudospectra Using ARPACK and Eigs
SIAM Journal on Scientific Computing
Parallel computation of pseudospectra of large sparse matrices
Parallel Computing - Parallel matrix algorithms and applications
FALCON: A MATLAB Interactive Restructuring Compiler
LCPC '95 Proceedings of the 8th International Workshop on Languages and Compilers for Parallel Computing
The design of a distributed MATLAB-based environment for computing pseudospectra
Future Generation Computer Systems - Special section: Complex problem-solving environments for grid computing
The design of a distributed MATLAB-based environment for computing pseudospectra
Future Generation Computer Systems - Special section: Complex problem-solving environments for grid computing
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One of the most computationally expensive problems in numerical linear algebra is the computation of the 驴-pseudospectrum of matrices, that is, the locus of eigenvalues of all matrices of the form A + E, where ||E|| 驴 驴. Several research efforts have been attempting to make the problem tractable by means of better algorithms and utilization of all possible computational resources. One common goal is to bring to users the power to extract pseudospectrum information from their applications, on the computational environments they generally use, at a cost that is sufficiently low to render these computations routine. To this end, we investigate a scheme based on i) iterative methods for computing pseudospectra via approximations of the resolvent norm, with ii) a computational platform based on a cluster of PCs and iii) a programming environment based on MATLAB enhanced with MPI functionality and show that it can achieve high performance for problems of significant size.