Scaling of general quadratic matrix equations
A scaling framework for general quadratic algebraic matrix equations is presented. All algebraic quadratic equations can be considered as special cases of a single generalized algebraic quadratic matrix equation (GQME). Hence, the paper is focused on the analysis and solution of the scaling problem...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2006
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| _version_ | 1797095552202047488 |
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| author | Tsachouridis, V Kouvaritakis, B Konstantinov, M Petkov, P |
| author_facet | Tsachouridis, V Kouvaritakis, B Konstantinov, M Petkov, P |
| author_sort | Tsachouridis, V |
| collection | OXFORD |
| description | A scaling framework for general quadratic algebraic matrix equations is presented. All algebraic quadratic equations can be considered as special cases of a single generalized algebraic quadratic matrix equation (GQME). Hence, the paper is focused on the analysis and solution of the scaling problem of that GQME. The presented scaling method is based on the assignment of predetermined values of the coefficients and the unknown matrices of the GQME. The proposed framework is independent of any numerical method and therefore its use is general. Implementations are presented for the special case of matrix algebraic Riccati equations (AREs). Some new results of matrix algebraic identities considering Kronecker and Hadamard products are also reported. |
| first_indexed | 2024-03-07T04:29:29Z |
| format | Journal article |
| id | oxford-uuid:cdd3feee-2c0e-4840-b0b5-70f018013109 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:29:29Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:cdd3feee-2c0e-4840-b0b5-70f0180131092022-03-27T07:31:25ZScaling of general quadratic matrix equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cdd3feee-2c0e-4840-b0b5-70f018013109EnglishSymplectic Elements at Oxford2006Tsachouridis, VKouvaritakis, BKonstantinov, MPetkov, PA scaling framework for general quadratic algebraic matrix equations is presented. All algebraic quadratic equations can be considered as special cases of a single generalized algebraic quadratic matrix equation (GQME). Hence, the paper is focused on the analysis and solution of the scaling problem of that GQME. The presented scaling method is based on the assignment of predetermined values of the coefficients and the unknown matrices of the GQME. The proposed framework is independent of any numerical method and therefore its use is general. Implementations are presented for the special case of matrix algebraic Riccati equations (AREs). Some new results of matrix algebraic identities considering Kronecker and Hadamard products are also reported. |
| spellingShingle | Tsachouridis, V Kouvaritakis, B Konstantinov, M Petkov, P Scaling of general quadratic matrix equations |
| title | Scaling of general quadratic matrix equations |
| title_full | Scaling of general quadratic matrix equations |
| title_fullStr | Scaling of general quadratic matrix equations |
| title_full_unstemmed | Scaling of general quadratic matrix equations |
| title_short | Scaling of general quadratic matrix equations |
| title_sort | scaling of general quadratic matrix equations |
| work_keys_str_mv | AT tsachouridisv scalingofgeneralquadraticmatrixequations AT kouvaritakisb scalingofgeneralquadraticmatrixequations AT konstantinovm scalingofgeneralquadraticmatrixequations AT petkovp scalingofgeneralquadraticmatrixequations |