## 抄録

Consider computing simple eigenvalues of a given compact infinite matrix re- garded as operating in the complex Hilbert space l^{2} by computing the eigenvalues of the truncated finite matrices and taking an obvious limit. In this paper we deal with a special case where the given matrix is compact, complex, and symmetric (but not necessarily Hermitian). Two examples of application are studied. The first is con- cerned with the equation J_{0}(z) - iJ_{1}(z)=0 appearing in the analysis of the solitary-wave runup on a sloping beach, and the second with the zeros of the Bessel function J_{m}(z) of any real order m. In each case, the problem is reformulated as an eigenvalue problem for a compact complex symmetric tridiagonal matrix operator in l^{2} whose eigenvalues are all simple. A complete error analysis for the numerical solution by truncation is given, based on the general theorems proved in this paper, where the usefulness of the seldom used generalized Rayleigh quotient is demonstrated.

本文言語 | English |
---|---|

ページ（範囲） | 35-70 |

ページ数 | 36 |

ジャーナル | Linear Algebra and Its Applications |

巻 | 194 |

号 | C |

DOI | |

出版ステータス | Published - 1993 11月 15 |

外部発表 | はい |

## ASJC Scopus subject areas

- 代数と数論
- 数値解析
- 幾何学とトポロジー
- 離散数学と組合せ数学

## フィンガープリント

「The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of J_{0}(z) - iJ

_{1}(z) and of Bessel functions J

_{m}(z) of any real order m」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。