Pseudospectra Gateway. Eigenvalue analysis of non-hermitian matrices and operators can be misleading: Predictions often fail to match observations. Specifically, trouble may arise when the associated sets of eigenvectors are ill-conditioned with respect to the norm of applied interest. In the case of the familiar Euclidean or 2-norm, this means that the matrix or operator is non-normal, and the eigenvectors are not orthogonal. Pseudospectra provide an analytical and graphical alternative for investigating non-normal matrices and operators. Follow the links below to find out more, and please email us with suggestions for additions and improvements

References in zbMATH (referenced in 17 articles )

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  1. Dhara, Kousik; Kulkarni, S. H.: Decomposition of the ((n,\epsilon))-pseudospectrum of an element of a Banach algebra (2020)
  2. Dhara, Kousik; Kulkarni, S. H.; Seidel, Markus: Continuity of the ((n,\epsilon))-pseudospectrum in Banach algebras (2019)
  3. Dhara, Kousik; Kulkarni, S. H.: The ((n,\epsilon))-pseudospectrum of an element of a Banach algebra (2018)
  4. Kestyn, James; Polizzi, Eric; Tang, Ping Tak Peter: Feast eigensolver for non-Hermitian problems (2016)
  5. Fatouros, Stavros; Psarrakos, Panayiotis: An improved grid method for the computation of the pseudospectra of matrix polynomials (2009)
  6. Brown, Nathanial P.: Quasi-diagonality and the finite section method (2007)
  7. Psarrakos, Panayiotis J.: A distance bound for pseudospectra of matrix polynomials (2007)
  8. Brown, Nathanial P.: AF embeddings and the numerical computation of spectra in irrational rotation algebras (2006)
  9. Du, Kui: A note on properties and computations of matrix pseudospectra (2006)
  10. Du, Kui; Wei, Yimin: Structured pseudospectra and structured sensitivity of eigenvalues (2006)
  11. Rump, Siegfried M.: Eigenvalues, pseudospectrum and structured perturbations (2006)
  12. Davies, E. B.: Semi-classical analysis and pseudo-spectra (2005)
  13. Malyshev, A. N.; Sadkane, M.: Componentwise pseudospectrum of a matrix (2004)
  14. Faber, Vance; Greenbaum, Anne; Marshall, Donald E.: The polynomial numerical hulls of Jordan blocks and related matrices. (2003)
  15. Meseguer, Á.; Trefethen, L. N.: Linearized pipe flow to Reynolds number (10^7). (2003)
  16. Böttcher, A.; Grudsky, S. M.: Can spectral value sets of Toeplitz band matrices jump? (2002)
  17. Higham, Nicholas J.; Tisseur, Françoise: More on pseudospectra for polynomial eigenvalue problems and applications in control theory (2002)