Accurate Computations with Generalized Pascal <i>k</i>-Eliminated Functional Matrices
This paper presents an accurate method to obtain the bidiagonal decomposition of some generalized Pascal matrices, including Pascal <i>k</i>-eliminated functional matrices and Pascal symmetric functional matrices. Sufficient conditions to assure that these matrices are either totally pos...
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/2/303 |
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| author | Jorge Delgado Héctor Orera Juan Manuel Peña |
| author_facet | Jorge Delgado Héctor Orera Juan Manuel Peña |
| author_sort | Jorge Delgado |
| collection | DOAJ |
| description | This paper presents an accurate method to obtain the bidiagonal decomposition of some generalized Pascal matrices, including Pascal <i>k</i>-eliminated functional matrices and Pascal symmetric functional matrices. Sufficient conditions to assure that these matrices are either totally positive or inverse of totally positive matrices are provided. In these cases, the presented method can be used to compute their eigenvalues, singular values and inverses with high relative accuracy. Numerical examples illustrate the high accuracy of our approach. |
| format | Article |
| id | doaj-art-8826dc327c6b4ea5954d69cb48cf7c60 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-8826dc327c6b4ea5954d69cb48cf7c602025-01-24T13:40:06ZengMDPI AGMathematics2227-73902025-01-0113230310.3390/math13020303Accurate Computations with Generalized Pascal <i>k</i>-Eliminated Functional MatricesJorge Delgado0Héctor Orera1Juan Manuel Peña2Departamento de Matemática Aplicada, Universidad de Zaragoza, 50018 Zaragoza, SpainDepartamento de Matemática Aplicada, Universidad de Zaragoza, 50009 Zaragoza, SpainDepartamento de Matemática Aplicada, Universidad de Zaragoza, 50009 Zaragoza, SpainThis paper presents an accurate method to obtain the bidiagonal decomposition of some generalized Pascal matrices, including Pascal <i>k</i>-eliminated functional matrices and Pascal symmetric functional matrices. Sufficient conditions to assure that these matrices are either totally positive or inverse of totally positive matrices are provided. In these cases, the presented method can be used to compute their eigenvalues, singular values and inverses with high relative accuracy. Numerical examples illustrate the high accuracy of our approach.https://www.mdpi.com/2227-7390/13/2/303bidiagonal decompositionhigh relative accuracytotal positivityk-eliminated Pascal matrix |
| spellingShingle | Jorge Delgado Héctor Orera Juan Manuel Peña Accurate Computations with Generalized Pascal <i>k</i>-Eliminated Functional Matrices Mathematics bidiagonal decomposition high relative accuracy total positivity k-eliminated Pascal matrix |
| title | Accurate Computations with Generalized Pascal <i>k</i>-Eliminated Functional Matrices |
| title_full | Accurate Computations with Generalized Pascal <i>k</i>-Eliminated Functional Matrices |
| title_fullStr | Accurate Computations with Generalized Pascal <i>k</i>-Eliminated Functional Matrices |
| title_full_unstemmed | Accurate Computations with Generalized Pascal <i>k</i>-Eliminated Functional Matrices |
| title_short | Accurate Computations with Generalized Pascal <i>k</i>-Eliminated Functional Matrices |
| title_sort | accurate computations with generalized pascal i k i eliminated functional matrices |
| topic | bidiagonal decomposition high relative accuracy total positivity k-eliminated Pascal matrix |
| url | https://www.mdpi.com/2227-7390/13/2/303 |
| work_keys_str_mv | AT jorgedelgado accuratecomputationswithgeneralizedpascalikieliminatedfunctionalmatrices AT hectororera accuratecomputationswithgeneralizedpascalikieliminatedfunctionalmatrices AT juanmanuelpena accuratecomputationswithgeneralizedpascalikieliminatedfunctionalmatrices |