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ファイル | 記述 | サイズ | フォーマット | |
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2174-13.pdf | 8.09 MB | Adobe PDF | 見る/開く |
タイトル: | An inversion algorithm for recovering a coefficient of Sturm-Liouville operator (Analysis of inverse problems through partial differential equations and related topics) |
著者: | Jiang, Xiaoying Xu, Xiang |
キーワード: | lnvesre Sturm-Liouville Problem Trace formulae Line search Newton-like Method 45C305 34L16 |
発行日: | Feb-2021 |
出版者: | 京都大学数理解析研究所 |
誌名: | 数理解析研究所講究録 |
巻: | 2174 |
開始ページ: | 115 |
終了ページ: | 128 |
抄録: | In this paper, an efficient algorithm for recovering a density of Sturm-Liouville operator from given two spectra is investigated. Based on Lidskii's theorem and Mercer's theorem, we build a sequence of trace formulae which bridge explicitly the density and eigenvalues in terms of nonlinear Fredholm integral equations. Due to intrinsic difficulties on ill-posedness of an inverse spectral problem, a truncated Fourier series regularization method is utilized for reconstructing the unknown density. Moreover, shifted Legendre polynomials are carried to balance the different order of trace formulae. Numerical results are presented to illustrated the effectiveness and stability of the proposed reconstruction algorithm. |
URI: | http://hdl.handle.net/2433/263961 |
出現コレクション: | 2174 偏微分方程式による逆問題解析とその周辺 |
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