Generalizing Eigenvalue Theorems to Pseudospectra Theorems
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...
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| Format: | Report |
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Unspecified
2000
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| Summary: | 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. |
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