The homogeneous projective transformation of general quadratic matrix equations
Algebraic quadratic equations are a special case of a single generalized algebraic quadratic matrix equation (GQME). Hence, the importance of that equation in science and engineering is evident. This paper focus on the study of solutions of that GQME and a unified framework for the characterization...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2005
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| _version_ | 1826264092468314112 |
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| author | Tsachouridis, V Kouvaritakis, B |
| author_facet | Tsachouridis, V Kouvaritakis, B |
| author_sort | Tsachouridis, V |
| collection | OXFORD |
| description | Algebraic quadratic equations are a special case of a single generalized algebraic quadratic matrix equation (GQME). Hence, the importance of that equation in science and engineering is evident. This paper focus on the study of solutions of that GQME and a unified framework for the characterization and identification of solutions at infinity and of finite solutions of general quadratic algebraic matrix equations is presented. The analysis is based on the concept of homogeneous projective transformation for general polynomial systems (Morgan, 1986). In addition, a numerical error analysis for the computed solutions is provided for the assessment of numerical accuracy, stability and conditioning of the computed solutions. The proposed framework is independent of any numerical method and therefore it can be used along with various possible numerical methods for the GQME solution, especially matrix flow-based algorithms (Chu, 1994) (e.g. continuation/ homotopy, Morgan, 1989). © The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. |
| first_indexed | 2024-03-06T20:02:13Z |
| format | Journal article |
| id | oxford-uuid:27b1be0c-6034-4f82-b603-8268bf3b815f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:02:13Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | oxford-uuid:27b1be0c-6034-4f82-b603-8268bf3b815f2022-03-26T12:08:30ZThe homogeneous projective transformation of general quadratic matrix equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:27b1be0c-6034-4f82-b603-8268bf3b815fEnglishSymplectic Elements at Oxford2005Tsachouridis, VKouvaritakis, BAlgebraic quadratic equations are a special case of a single generalized algebraic quadratic matrix equation (GQME). Hence, the importance of that equation in science and engineering is evident. This paper focus on the study of solutions of that GQME and a unified framework for the characterization and identification of solutions at infinity and of finite solutions of general quadratic algebraic matrix equations is presented. The analysis is based on the concept of homogeneous projective transformation for general polynomial systems (Morgan, 1986). In addition, a numerical error analysis for the computed solutions is provided for the assessment of numerical accuracy, stability and conditioning of the computed solutions. The proposed framework is independent of any numerical method and therefore it can be used along with various possible numerical methods for the GQME solution, especially matrix flow-based algorithms (Chu, 1994) (e.g. continuation/ homotopy, Morgan, 1989). © The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. |
| spellingShingle | Tsachouridis, V Kouvaritakis, B The homogeneous projective transformation of general quadratic matrix equations |
| title | The homogeneous projective transformation of general quadratic matrix equations |
| title_full | The homogeneous projective transformation of general quadratic matrix equations |
| title_fullStr | The homogeneous projective transformation of general quadratic matrix equations |
| title_full_unstemmed | The homogeneous projective transformation of general quadratic matrix equations |
| title_short | The homogeneous projective transformation of general quadratic matrix equations |
| title_sort | homogeneous projective transformation of general quadratic matrix equations |
| work_keys_str_mv | AT tsachouridisv thehomogeneousprojectivetransformationofgeneralquadraticmatrixequations AT kouvaritakisb thehomogeneousprojectivetransformationofgeneralquadraticmatrixequations AT tsachouridisv homogeneousprojectivetransformationofgeneralquadraticmatrixequations AT kouvaritakisb homogeneousprojectivetransformationofgeneralquadraticmatrixequations |