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Convergence rates and explicit error bounds of Hill's method for spectra of self-Adjoint differential operators
http://hdl.handle.net/10445/7720
http://hdl.handle.net/10445/7720f18227f2-c5fb-42e2-9464-f750d10bb938
| Item type | 学術雑誌論文 / Journal Article(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2014-09-03 | |||||
| タイトル | ||||||
| タイトル | Convergence rates and explicit error bounds of Hill's method for spectra of self-Adjoint differential operators | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | journal article | |||||
| アクセス権 | ||||||
| アクセス権 | metadata only access | |||||
| アクセス権URI | http://purl.org/coar/access_right/c_14cb | |||||
| 著者 |
田中, 健一郎
× 田中, 健一郎 |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | We present the convergence rates and the explicit error bounds of Hill’s method, which is a numerical method for computing the spectra of ordinary differential operators with periodic coefficients. This method approximates the operator by a finite dimensional matrix. On the assumption that the operator is self-adjoint, it is shown that, under some conditions, we can obtain the convergence rates of eigenvalues with respect to the dimension and the explicit error bounds. Numerical examples demonstrate that we can verify these conditions using Gershgorin’s theorem for some real problems. Main theorems are proved using the Dunford integrals which project an vector to a specific eigenspace. | |||||
| 書誌情報 |
Japan Journal of Industrial and Applied Mathematics 巻 31, 号 1, p. 25-56, 発行日 2014 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 09167005 | |||||
| 査読有無 | ||||||
| 値 | あり/yes | |||||
| 研究業績種別 | ||||||
| 値 | 原著論文/Original Paper | |||||
| 単著共著 | ||||||
| 値 | 共著/joint | |||||
| 出版者 | ||||||
| 出版者 | Springer Japan | |||||
