Approximating the weighted pseudospectra of large matrices
In different applications it is necessary to compute the pseudospectra of matrices in an energy or weighted norm. In this work we develop a practical method to convert an Arnoldi factorization based on the Euclidean inner product into another Arnoldi factorization in a weighted inner product. We also propose how to use this approach to find a portion of the weighted pseudospectra of large matrices. Numerical results on different test problems are presented. (c) 2011 Elsevier Ltd. All rights reserved.
spectrum pseudospectrum weighted pseudospectrum arnoldi method weighted arnoldi factorization