An Algorithm to Construct a Tridiagonal Matrix Factored by Bidiagonal Matrices with Prescribed Eigenvalues and Specified Entries
This paper presents an algorithm to construct a tridiagonal matrix factored by bidiagonal matrices with prescribed eigenvalues and specified matrix entries. The proposed algorithm addresses inverse eigenvalue problems (IEPs) constrained by LR decomposition. Using techniques from discrete soliton th...
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ITB Journal Publisher
2025-04-01
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| Series: | Journal of Mathematical and Fundamental Sciences |
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| Online Access: | https://journals.itb.ac.id/index.php/jmfs/article/view/25269 |
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| author | Koichi Kondo |
| author_facet | Koichi Kondo |
| author_sort | Koichi Kondo |
| collection | DOAJ |
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This paper presents an algorithm to construct a tridiagonal matrix factored by bidiagonal matrices with prescribed eigenvalues and specified matrix entries. The proposed algorithm addresses inverse eigenvalue problems (IEPs) constrained by LR decomposition. Using techniques from discrete soliton theory, we derive recurrence relations that connect matrix entries and eigenvalues. The algorithm systematically computes unknown entries in the matrix from given spectrum data and partial matrix information. Several examples, including cases with real, complex, and multiple eigenvalues, demonstrate the efficiency of the proposed algorithm. Additionally, we provide conditions under which the algorithm successfully solves the IEP.
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| format | Article |
| id | doaj-art-ee3e4b9cf0784debbaf90a9cfc16e3d1 |
| institution | OA Journals |
| issn | 2337-5760 2338-5510 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | ITB Journal Publisher |
| record_format | Article |
| series | Journal of Mathematical and Fundamental Sciences |
| spelling | doaj-art-ee3e4b9cf0784debbaf90a9cfc16e3d12025-08-20T02:34:32ZengITB Journal PublisherJournal of Mathematical and Fundamental Sciences2337-57602338-55102025-04-0156310.5614/j.math.fund.sci.2024.56.3.5An Algorithm to Construct a Tridiagonal Matrix Factored by Bidiagonal Matrices with Prescribed Eigenvalues and Specified EntriesKoichi Kondo0Graduate School of Science and Engineering, Doshisha University, Tatara-Miyakodani 1-3, Kyotanabe, Kyoto 610-0394, Japan This paper presents an algorithm to construct a tridiagonal matrix factored by bidiagonal matrices with prescribed eigenvalues and specified matrix entries. The proposed algorithm addresses inverse eigenvalue problems (IEPs) constrained by LR decomposition. Using techniques from discrete soliton theory, we derive recurrence relations that connect matrix entries and eigenvalues. The algorithm systematically computes unknown entries in the matrix from given spectrum data and partial matrix information. Several examples, including cases with real, complex, and multiple eigenvalues, demonstrate the efficiency of the proposed algorithm. Additionally, we provide conditions under which the algorithm successfully solves the IEP. https://journals.itb.ac.id/index.php/jmfs/article/view/25269determinant expressiondiscrete soliton theoryinverse eigenvalue problemLR decompositiontridiagonal matrix |
| spellingShingle | Koichi Kondo An Algorithm to Construct a Tridiagonal Matrix Factored by Bidiagonal Matrices with Prescribed Eigenvalues and Specified Entries Journal of Mathematical and Fundamental Sciences determinant expression discrete soliton theory inverse eigenvalue problem LR decomposition tridiagonal matrix |
| title | An Algorithm to Construct a Tridiagonal Matrix Factored by Bidiagonal Matrices with Prescribed Eigenvalues and Specified Entries |
| title_full | An Algorithm to Construct a Tridiagonal Matrix Factored by Bidiagonal Matrices with Prescribed Eigenvalues and Specified Entries |
| title_fullStr | An Algorithm to Construct a Tridiagonal Matrix Factored by Bidiagonal Matrices with Prescribed Eigenvalues and Specified Entries |
| title_full_unstemmed | An Algorithm to Construct a Tridiagonal Matrix Factored by Bidiagonal Matrices with Prescribed Eigenvalues and Specified Entries |
| title_short | An Algorithm to Construct a Tridiagonal Matrix Factored by Bidiagonal Matrices with Prescribed Eigenvalues and Specified Entries |
| title_sort | algorithm to construct a tridiagonal matrix factored by bidiagonal matrices with prescribed eigenvalues and specified entries |
| topic | determinant expression discrete soliton theory inverse eigenvalue problem LR decomposition tridiagonal matrix |
| url | https://journals.itb.ac.id/index.php/jmfs/article/view/25269 |
| work_keys_str_mv | AT koichikondo analgorithmtoconstructatridiagonalmatrixfactoredbybidiagonalmatriceswithprescribedeigenvaluesandspecifiedentries AT koichikondo algorithmtoconstructatridiagonalmatrixfactoredbybidiagonalmatriceswithprescribedeigenvaluesandspecifiedentries |