Bibliographic Citation
| Document |  911 K |
|---|---|
| DOI | 10.2172/10184297 |
| Title | A sharp upper bound for departure from normality |
| Creator/Author | Lee, S.L. |
| Publication Date | 1993 Aug 01 |
| OSTI Identifier | OSTI ID: 10184297; Legacy ID: DE93040457 |
| Report Number(s) | ORNL/TM--12426 |
| DOE Contract Number | AC05-84OR21400 |
| Other Number(s) | Other: ON: DE93040457 |
| Resource Type | Technical Report |
| Coverage | Topical |
| Resource Relation | Other Information: PBD: Aug 1993 |
| Research Org | Oak Ridge National Lab., TN (United States) |
| Sponsoring Org | USDOE, Washington, DC (United States) |
| Subject | 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; MATRICES; CALCULATION METHODS; EIGENVALUES; HERMITIAN MATRIX |
| Description/Abstract | The departure from normality of a matrix is a real scalar that is impractical to compute if a matrix is large and its eigenvalues are unknown. A simple formula is presented for computing an upper bound for departure from normality in the Frobenius norm. This new upper bound is cheaper to compute than the upper bound derived by Henrici. Moreover, the new bound is sharp for Hermitian matrices, skew-Hermitian matrices and, in general, any matrix with eigenvalues that are horizontally or vertically aligned in the complex plane. In terms of applications, the new bound can be used in computing bounds for the spectral norm of matrix functions or bounds for the sensitivity of eigenvalues to matrix perturbations. |
| Country of Publication | United States |
| Language | English |
| Format | Medium: ED; Size: 18 p. |
| Availability | OSTI; NTIS; GPO Dep. |
| System Entry Date | 2008 Feb 12 |
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