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| Content Provider | Springer Nature Link |
|---|---|
| Author | Ishiwata, Emiko Fukuda, Akiko Nakamura, Yoshimasa Iwasaki, Masashi Yamamoto, Yusaku |
| Copyright Year | 2011 |
| Abstract | Recently, some of the authors designed an algorithm, named the dhLV algorithm, for computing complex eigenvalues of a certain class of band matrix. The recursion formula of the dhLV algorithm is based on the discrete hungry Lotka–Volterra (dhLV) system, which is an integrable system. One of the authors has proposed an algorithm, named the multiple dqd algorithm, for computing eigenvalues of a totally nonnegative (TN) band matrix. In this paper, by introducing a theorem on matrix eigenvalues, we first show that the eigenvalues of a TN matrix are also computable by the dhLV algorithm. We next clarify the asymptotic behavior of the discrete hungry Toda (dhToda) equation, which is also an integrable system, and show that a similarity transformation for a TN matrix is given through the dhToda equation. Then, by combining these properties of the dhToda equation, we design a new algorithm, named the dhToda algorithm, for computing eigenvalues of a TN matrix. We also describe the close relationship among the above three algorithms and give numerical examples. |
| Ending Page | 445 |
| Page Count | 23 |
| Starting Page | 423 |
| File Format | |
| ISSN | 03733114 |
| e-ISSN | 16181891 |
| Journal | Annali di Matematica Pura ed Applicata |
| Issue Number | 3 |
| Volume Number | 192 |
| Language | English |
| Publisher | Springer-Verlag |
| Publisher Date | 2011-11-13 |
| Publisher Place | Berlin, Heidelberg |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) Matrix eigenvalue Soliton theory, asymptotic behavior of solutions Similarity transformation Eigenvalues, eigenvectors Mathematics Discrete hungry Lotka–Volterra system Discrete hungry Toda equation |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
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