Pseudospectrum
In mathematics, the pseudospectrum of an operator is a set containing the spectrum of the operator and the numbers that are "almost" eigenvalues. Knowledge of the pseudospectrum can be particularly useful for understanding non-normal operators and their eigenfunctions.
The ε-pseudospectrum of a matrix A consists of all eigenvalues of matrices which are ε-close to A:[1]
Numerical algorithms which calculate the eigenvalues of a matrix give only approximate results due to rounding and other errors. These errors can be described with the matrix E.
References[]
- ^ Hogben, Leslie (2013). Handbook of Linear Algebra, Second Edition. CRC Press. p. 23-1. ISBN 9781466507296. Retrieved 8 September 2017.
- Lloyd N. Trefethen and Mark Embree: "Spectra And Pseudospectra: The Behavior of Nonnormal Matrices And Operators", Princeton Univ. Press, ISBN 978-0691119465 (2005).
- Pseudospectra Gateway / Embree and Trefethen [1]
Categories:
- Numerical linear algebra
- Spectral theory