✦ LIBER ✦
Short note: An integrable numerical algorithm for computing eigenvalues of a specially structured matrix
✍ Scribed by Jian-Qing Sun; Xing-Biao Hu; Hon-Wah Tam
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 123 KB
- Volume
- 18
- Category
- Article
- ISSN
- 1070-5325
- DOI
- 10.1002/nla.754
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✦ Synopsis
This paper is motivated by some recent work of Fukuda, Ishiwata, Iwasaki, and Nakamura (Inverse Problems 2009; 25:015007). We first design an algorithm for computing the eigenvalues of a specially structured matrix from the discrete Bogoyavlensky Lattice 2 (dBL2) system. A Lax representation for the dBL2 system is given in a matrix form. By considering the asymptotic behavior of dBL2 variables, some characteristic polynomials are then factorized. A new algorithm for computing the complex eigenvalues of a specially structured matrix is then introduced.