Recursive Matrix Calculation Paradigm by the Example of Structured Matrix
In this paper, we derive recursive algorithms for calculating the determinant and inverse of the generalized Vandermonde matrix. The main advantage of the recursive algorithms is the fact that the computational complexity of the presented algorithm is better than calculating the determinant and the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-01-01
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| Series: | Information |
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| Online Access: | https://www.mdpi.com/2078-2489/11/1/42 |
| _version_ | 1819199103100256256 |
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| author | Jerzy S. Respondek |
| author_facet | Jerzy S. Respondek |
| author_sort | Jerzy S. Respondek |
| collection | DOAJ |
| description | In this paper, we derive recursive algorithms for calculating the determinant and inverse of the generalized Vandermonde matrix. The main advantage of the recursive algorithms is the fact that the computational complexity of the presented algorithm is better than calculating the determinant and the inverse by means of classical methods, developed for the general matrices. The results of this article do not require any symbolic calculations and, therefore, can be performed by a numerical algorithm implemented in a specialized (like Matlab or Mathematica) or general-purpose programming language (C, C++, Java, Pascal, Fortran, etc.). |
| first_indexed | 2024-12-23T03:11:01Z |
| format | Article |
| id | doaj.art-d7aa5347a37641d881bc3c824b82cd03 |
| institution | Directory Open Access Journal |
| issn | 2078-2489 |
| language | English |
| last_indexed | 2024-12-23T03:11:01Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Information |
| spelling | doaj.art-d7aa5347a37641d881bc3c824b82cd032022-12-21T18:02:15ZengMDPI AGInformation2078-24892020-01-011114210.3390/info11010042info11010042Recursive Matrix Calculation Paradigm by the Example of Structured MatrixJerzy S. Respondek0Institute of Computer Science, Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, PolandIn this paper, we derive recursive algorithms for calculating the determinant and inverse of the generalized Vandermonde matrix. The main advantage of the recursive algorithms is the fact that the computational complexity of the presented algorithm is better than calculating the determinant and the inverse by means of classical methods, developed for the general matrices. The results of this article do not require any symbolic calculations and, therefore, can be performed by a numerical algorithm implemented in a specialized (like Matlab or Mathematica) or general-purpose programming language (C, C++, Java, Pascal, Fortran, etc.).https://www.mdpi.com/2078-2489/11/1/42numerical recipesnumerical algebralinear algebramatrix inversegeneralized vandermonde matrixc++ |
| spellingShingle | Jerzy S. Respondek Recursive Matrix Calculation Paradigm by the Example of Structured Matrix Information numerical recipes numerical algebra linear algebra matrix inverse generalized vandermonde matrix c++ |
| title | Recursive Matrix Calculation Paradigm by the Example of Structured Matrix |
| title_full | Recursive Matrix Calculation Paradigm by the Example of Structured Matrix |
| title_fullStr | Recursive Matrix Calculation Paradigm by the Example of Structured Matrix |
| title_full_unstemmed | Recursive Matrix Calculation Paradigm by the Example of Structured Matrix |
| title_short | Recursive Matrix Calculation Paradigm by the Example of Structured Matrix |
| title_sort | recursive matrix calculation paradigm by the example of structured matrix |
| topic | numerical recipes numerical algebra linear algebra matrix inverse generalized vandermonde matrix c++ |
| url | https://www.mdpi.com/2078-2489/11/1/42 |
| work_keys_str_mv | AT jerzysrespondek recursivematrixcalculationparadigmbytheexampleofstructuredmatrix |