Bidiagonalization of (k, k + 1)-tridiagonal matrices
In this paper,we present the bidiagonalization of n-by-n (k, k+1)-tridiagonal matriceswhen n < 2k. Moreover,we show that the determinant of an n-by-n (k, k+1)-tridiagonal matrix is the product of the diagonal elements and the eigenvalues of the matrix are the diagonal elements. This paper is rela...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2019-01-01
|
| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/spma-2019-0002 |
| _version_ | 1819044893117382656 |
|---|---|
| author | Takahira S. Sogabe T. Usuda T.S. |
| author_facet | Takahira S. Sogabe T. Usuda T.S. |
| author_sort | Takahira S. |
| collection | DOAJ |
| description | In this paper,we present the bidiagonalization of n-by-n (k, k+1)-tridiagonal matriceswhen n < 2k. Moreover,we show that the determinant of an n-by-n (k, k+1)-tridiagonal matrix is the product of the diagonal elements and the eigenvalues of the matrix are the diagonal elements. This paper is related to the fast block diagonalization algorithm using the permutation matrix from [T. Sogabe and M. El-Mikkawy, Appl. Math. Comput., 218, (2011), 2740-2743] and [A. Ohashi, T. Sogabe, and T. S. Usuda, Int. J. Pure and App. Math., 106, (2016), 513-523]. |
| first_indexed | 2024-12-21T10:19:54Z |
| format | Article |
| id | doaj.art-007af5e4abce4cd188c6a30657ffd6c8 |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-12-21T10:19:54Z |
| publishDate | 2019-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-007af5e4abce4cd188c6a30657ffd6c82022-12-21T19:07:28ZengDe GruyterSpecial Matrices2300-74512019-01-0171202610.1515/spma-2019-0002spma-2019-0002Bidiagonalization of (k, k + 1)-tridiagonal matricesTakahira S.0Sogabe T.1Usuda T.S.2Graduate School of Information Science & Technology, Aichi Prefectural University,Toyota, JapanGraduate School of Engineering, Nagoya University,Toyota, JapanSchool of Information Science & Technology, Aichi Prefectural University,Toyota, JapanIn this paper,we present the bidiagonalization of n-by-n (k, k+1)-tridiagonal matriceswhen n < 2k. Moreover,we show that the determinant of an n-by-n (k, k+1)-tridiagonal matrix is the product of the diagonal elements and the eigenvalues of the matrix are the diagonal elements. This paper is related to the fast block diagonalization algorithm using the permutation matrix from [T. Sogabe and M. El-Mikkawy, Appl. Math. Comput., 218, (2011), 2740-2743] and [A. Ohashi, T. Sogabe, and T. S. Usuda, Int. J. Pure and App. Math., 106, (2016), 513-523].https://doi.org/10.1515/spma-2019-0002(kk + 1)-tridiagonal matrixbidiagonalizationeigenvaluesprimary 65f15secondary 65f30 |
| spellingShingle | Takahira S. Sogabe T. Usuda T.S. Bidiagonalization of (k, k + 1)-tridiagonal matrices Special Matrices (k k + 1)-tridiagonal matrix bidiagonalization eigenvalues primary 65f15 secondary 65f30 |
| title | Bidiagonalization of (k, k + 1)-tridiagonal matrices |
| title_full | Bidiagonalization of (k, k + 1)-tridiagonal matrices |
| title_fullStr | Bidiagonalization of (k, k + 1)-tridiagonal matrices |
| title_full_unstemmed | Bidiagonalization of (k, k + 1)-tridiagonal matrices |
| title_short | Bidiagonalization of (k, k + 1)-tridiagonal matrices |
| title_sort | bidiagonalization of k k 1 tridiagonal matrices |
| topic | (k k + 1)-tridiagonal matrix bidiagonalization eigenvalues primary 65f15 secondary 65f30 |
| url | https://doi.org/10.1515/spma-2019-0002 |
| work_keys_str_mv | AT takahiras bidiagonalizationofkk1tridiagonalmatrices AT sogabet bidiagonalizationofkk1tridiagonalmatrices AT usudats bidiagonalizationofkk1tridiagonalmatrices |