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Pseudospectrum : ウィキペディア英語版
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'':
:\Lambda_\epsilon(A) = \^n \setminus \, \exists E \in \mathbb^ \colon (A+E)x = \lambda x, \|E\| \leq \epsilon \}.
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 ==

* Pseudospectra Gateway / Embree and Trefethen ()

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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