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A new method of convergence acceleration of series expansion for analytic functions in the complex domain
http://hdl.handle.net/10445/8042
http://hdl.handle.net/10445/804245034ff7-327f-4969-bd07-cb61ab50e525
| Item type | 学術雑誌論文 / Journal Article(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2015-03-26 | |||||
| タイトル | ||||||
| タイトル | A new method of convergence acceleration of series expansion for analytic functions in the complex domain | |||||
| 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 |
村重, 淳
× 村重, 淳× 田中, 健一郎 |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | This paper proposes a new method of convergence acceleration of series expansion of complex functions which are analytic on and inside the unit circle in the complex plane. This class of complex functions may have some singularities outside the unit circle, which dominate convergence of series expansion. In the proposed method, the singular points are moved away from the origin using conformal mapping, and the function is expanded using a sequence of polynomials orthogonalized on the boundary of the mapped complex domain. The decay rate of coefficients of the orthogonal polynomial expansion can be related to the convergence region in a similar form to the Cauchy–Hadamard formula for power series. Using this relation, we quantitatively evaluate and maximize the convergence rate of the improved series. Numerical examples demonstrate that the proposed method is effective for slow convergent series, and may converge faster than Padé approximants. | |||||
| 書誌情報 |
Japan Journal of Industrial and Applied Mathematics 巻 32, 号 1, p. 95-117, 発行日 2015-03 |
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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 | |||||
