Computing the spectral decomposition of interval matrices and a study on interval matrix power
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866909823896911872 |
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| author | Hartman, David Hladík, Milan Říha, David |
| author_facet | Hartman, David Hladík, Milan Říha, David |
| contents | We present an algorithm for computing a spectral decomposition of an interval matrix as an enclosure of spectral decompositions of particular realizations of interval matrices. The algorithm relies on tight outer estimations of eigenvalues and eigenvectors of corresponding interval matrices. We present a method for general interval matrices as well as its modification for symmetric interval matrices. As an illustration, we apply the spectral decomposition to computing powers of interval matrices. Numerical results suggest that a simple binary exponentiation is more efficient for smaller exponents, but our approach becomes better when computing higher powers or powers of a special type of matrices. In particular, we consider symmetric interval and circulant interval matrices. In both cases we utilize some properties of the corresponding classes of matrices to make the power computation more efficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_05275 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Computing the spectral decomposition of interval matrices and a study on interval matrix power Hartman, David Hladík, Milan Říha, David Numerical Analysis We present an algorithm for computing a spectral decomposition of an interval matrix as an enclosure of spectral decompositions of particular realizations of interval matrices. The algorithm relies on tight outer estimations of eigenvalues and eigenvectors of corresponding interval matrices. We present a method for general interval matrices as well as its modification for symmetric interval matrices. As an illustration, we apply the spectral decomposition to computing powers of interval matrices. Numerical results suggest that a simple binary exponentiation is more efficient for smaller exponents, but our approach becomes better when computing higher powers or powers of a special type of matrices. In particular, we consider symmetric interval and circulant interval matrices. In both cases we utilize some properties of the corresponding classes of matrices to make the power computation more efficient. |
| title | Computing the spectral decomposition of interval matrices and a study on interval matrix power |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1912.05275 |