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

Jian Qing Sun; Xing Biao Hu; Hon Wah TAM

doi:10.1002/nla.754

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

Department of Computer Science

Research output: Contribution to journal › Journal article › peer-review

5 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 language	English
Pages (from-to)	261-274
Number of pages	14
Journal	Numerical Linear Algebra with Applications
Volume	18
Issue number	2
DOIs	https://doi.org/10.1002/nla.754
Publication status	Published - 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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10.1002/nla.754

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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.",

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N2 - 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.

AB - 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.

KW - Asymptotic behavior

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KW - Lax form

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

Abstract

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