The Mathematical Institute, University of Oxford, Eprints Archive

Generalizing Eigenvalue Theorems to Pseudospectra Theorems

Embree, Mark and Trefethen, Lloyd N. (2000) Generalizing Eigenvalue Theorems to Pseudospectra Theorems. Technical Report. Unspecified. (Submitted)

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Abstract

Analysis of nonsymmetric matrix iterations based on eigenvalues can be misleading. In this paper, we discuss sixteen theorems involving $\epsilon$-pseudospectra that each generalize a familiar eigenvalue theorem and may provide more descriptive information in some cases. Our organizing principle is that each pseudospectral theorem reduces precisely to the corresponding eigenvalue theorem when $\epsilon$ = 0.

This work was supported by UK Engineering and Physical Sciences Research Council Grant GR/M12414.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Linear and multilinear algebra; matrix theory
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1269
Deposited By:Lotti Ekert
Deposited On:01 Jun 2011 09:22
Last Modified:01 Jun 2011 09:22

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