Short note: An integrable numerical algorithm for computing eigenvalues of a specially structured matrix

Jian Qing Sun, Xing Biao Hu*, Hon Wah TAM

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)261-274
Number of pages14
JournalNumerical Linear Algebra with Applications
Volume18
Issue number2
DOIs
Publication statusPublished - Mar 2011

Scopus Subject Areas

  • Algebra and Number Theory
  • Applied Mathematics

User-Defined Keywords

  • Asymptotic behavior
  • Complex eigenvalues
  • Discrete Bogoyavlensky system
  • Lax form

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