Large-Scale Computation of Pseudospectra Using ARPACK and Eigs

Authors:
Thomas G. Wright;Lloyd N. Trefethen
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2001

Citing 0
Cited 11

Parallel Computation of Pseudospectra Using Transfer Functions on a MATLAB-MPI Cluster Platform

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A pseudospectral mapping theorem

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Convergence and round-off errors in a two-dimensional eigenvalue problem using spectral methods and Arnoldi-Chebyshev algorithm

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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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On the generation of Krylov subspace bases

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Fast Algorithms for the Approximation of the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix

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Original article: A note on computation of pseudospectra

Mathematics and Computers in Simulation

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Abstract

ARPACK and its {\sc Matlab} counterpart, {\tt eigs}, are software packages that calculate some eigenvalues of a large nonsymmetric matrix by Arnoldi iteration with implicit restarts. We show that at a small additional cost, which diminishes relatively as the matrix dimension increases, good estimates of pseudospectra in addition to eigenvalues can be obtained as a by-product. Thus in large-scale eigenvalue calculations it is feasible to obtain routinely not just eigenvalue approximations, but also information as to whether or not the eigenvalues are likely to be physically significant. Examples are presented for matrices with dimension up to 200,000.