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Uniform approximation to finite Hilbert transform of oscillatory functions and its algorithm
http://hdl.handle.net/10098/0002000113
http://hdl.handle.net/10098/000200011339f3215f-c97e-485b-b2d7-c4805afa376a
名前 / ファイル | ライセンス | アクション |
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Item type | 学術雑誌論文 / Journal Article(1) | |||||||||
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公開日 | 2024-02-08 | |||||||||
タイトル | ||||||||||
言語 | en | |||||||||
タイトル | Uniform approximation to finite Hilbert transform of oscillatory functions and its algorithm | |||||||||
言語 | ||||||||||
言語 | eng | |||||||||
キーワード | ||||||||||
言語 | en | |||||||||
主題Scheme | Other | |||||||||
主題 | quadrature rule | |||||||||
キーワード | ||||||||||
言語 | en | |||||||||
主題Scheme | Other | |||||||||
主題 | Principal value integral | |||||||||
キーワード | ||||||||||
言語 | en | |||||||||
主題Scheme | Other | |||||||||
主題 | Oscillatory function | |||||||||
キーワード | ||||||||||
言語 | en | |||||||||
主題Scheme | Other | |||||||||
主題 | Chebyshev interpolation | |||||||||
キーワード | ||||||||||
言語 | en | |||||||||
主題Scheme | Other | |||||||||
主題 | Error analysis | |||||||||
キーワード | ||||||||||
言語 | en | |||||||||
主題Scheme | Other | |||||||||
主題 | Uniform approximation | |||||||||
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 | open access | |||||||||
アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||||
著者 |
Hasegawa, Takemitsu
× Hasegawa, Takemitsu
× Sugiura, Hiroshi
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抄録 | ||||||||||
内容記述タイプ | Abstract | |||||||||
内容記述 | For the finite Hilbert transform of oscillatory functions Q(f;c,ω)=f^1_-1 f(x) e^iωx / (x-c) dt with a smooth function f and real ω ≠ 0, for c ∈ (-1,1) in the sense of Cauchy principal value or for c=±1 of Hadamard finite-part, we present an approximation method of Clenshaw–Curtis type and its algorithm. Interpolating f by a polynomial pn of degree n and expanding in terms of the Chebyshev polynomials with O(n log n) operations by the FFT, we obtain an approximation Q(pn;c,ω) ≅ Q(f;c,ω). We write Q(pn;c,ω) as a sum of the sine and cosine integrals and an oscillatory integral of a polynomial of degree n-1. We efficiently evaluate the oscillatory integral with a combination of authors’ previous method and Keller’s method. For f(z) analytic on the interval [-1,1]in the complex plane z, the error of Q(pn;c,ω) is bounded uniformly with respect to c and ω. Numerical examples illustrate the performance of our method. | |||||||||
言語 | en | |||||||||
書誌情報 |
en : Journal of Computational and Applied Mathematics 巻 358, p. 327-342, 発行日 2019-10-01 |
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出版者 | ||||||||||
言語 | en | |||||||||
出版者 | Elsevier | |||||||||
ISSN | ||||||||||
収録物識別子タイプ | PISSN | |||||||||
収録物識別子 | 0377-0427 | |||||||||
ISSN | ||||||||||
収録物識別子タイプ | EISSN | |||||||||
収録物識別子 | 1879-1778 | |||||||||
DOI | ||||||||||
関連タイプ | isVersionOf | |||||||||
識別子タイプ | DOI | |||||||||
関連識別子 | https://doi.org/10.1016/j.cam.2019.02.012 | |||||||||
関連サイト | ||||||||||
関連タイプ | isVersionOf | |||||||||
識別子タイプ | URI | |||||||||
関連識別子 | https://www.sciencedirect.com/science/article/pii/S0377042719300858?via%3Dihub | |||||||||
言語 | en | |||||||||
関連名称 | Science Direct | |||||||||
著者版フラグ | ||||||||||
出版タイプ | AM | |||||||||
出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||||||
備考 | ||||||||||
ja | ||||||||||
Science Directにてオープンアーカイブ | ||||||||||
その他のID | ||||||||||
ja | ||||||||||
TD10126668 |