{"created":"2024-02-13T02:40:50.167677+00:00","id":2000117,"links":{},"metadata":{"_buckets":{"deposit":"c23287f3-e021-4d68-8ee5-8cd4260857df"},"_deposit":{"created_by":18,"id":"2000117","owner":"18","owners":[18],"pid":{"revision_id":0,"type":"depid","value":"2000117"},"status":"published"},"_oai":{"id":"oai:u-fukui.repo.nii.ac.jp:02000117","sets":["2403:2404"]},"author_link":[],"control_number":"2000117","item_10001_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2011-06-30","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicPageEnd":"252","bibliographicPageStart":"243","bibliographicVolumeNumber":"236","bibliographic_titles":[{"bibliographic_title":"Journal of Computational and Applied Mathematics","bibliographic_titleLang":"en"}]}]},"item_10001_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"Algorithms are proposed for the numerical evaluation of Cauchy principal value integrals ⨍^1_-1 ω(t) f (t) / (t－x)dt,－1＜ x ＜ 1, with weight functions of Jacobi type singularities ω (t)＝(1－t)^α (1＋t)^β, where α＝±1/2 and β＝±1/2, for a given function f(t) and Hadamard finite-part integrals ⨎^1_-1 ω(t) f (t) / (t－x)^dt. The function f is interpolated by using a finite sum of Chebyshev polynomials. The present algorithms require O(N log N) arithmetic operations, where N is the order of the interpolation polynomial. It is shown that the present scheme gives uniform approximations, namely the errors are bounded independently of x, and is very efficient for smooth f. Further, we discuss approximations of hyper-singular integrals ∫^1_-1 ω(t)f(t)/(t－x)^dt,n≥3, and show their uniform convergences. Numerical examples are given to demonstrate the performance of the present schemes.","subitem_description_language":"en","subitem_description_type":"Abstract"}]},"item_10001_publisher_8":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"Elsevier","subitem_publisher_language":"en"}]},"item_10001_relation_14":{"attribute_name":"DOI","attribute_value_mlt":[{"subitem_relation_type":"isVersionOf","subitem_relation_type_id":{"subitem_relation_type_id_text":"https://doi.org/10.1016/j.cam.2011.06.027","subitem_relation_type_select":"DOI"}}]},"item_10001_relation_17":{"attribute_name":"関連サイト","attribute_value_mlt":[{"subitem_relation_type":"isVersionOf","subitem_relation_type_id":{"subitem_relation_type_id_text":"https://www.sciencedirect.com/science/article/pii/S0377042711003633?via%3Dihub","subitem_relation_type_select":"URI"}}]},"item_10001_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"0377-0427","subitem_source_identifier_type":"PISSN"},{"subitem_source_identifier":"1879-1778","subitem_source_identifier_type":"EISSN"}]},"item_10001_text_25":{"attribute_name":"その他のID","attribute_value_mlt":[{"subitem_text_language":"ja","subitem_text_value":"TD10126672"}]},"item_10001_textarea_24":{"attribute_name":"備考","attribute_value_mlt":[{"subitem_textarea_language":"ja","subitem_textarea_value":"Science Directにてオープンアーカイブ"}]},"item_10001_version_type_20":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_ab4af688f83e57aa","subitem_version_type":"AM"}]},"item_access_right":{"attribute_name":"アクセス権","attribute_value_mlt":[{"subitem_access_right":"open access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_abf2"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Hasegawa, Takemitsu","creatorNameLang":"en"}]},{"creatorNames":[{"creatorName":"Sugiura, Hiroshi","creatorNameLang":"en"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_access","date":[{"dateType":"Available","dateValue":"2024-02-13"}],"filename":"BD10126672.pdf","filesize":[{"value":"144 KB"}],"format":"application/pdf","mimetype":"application/pdf","url":{"url":"https://u-fukui.repo.nii.ac.jp/record/2000117/files/BD10126672.pdf"},"version_id":"9c2f9f7d-be76-4737-8224-e921d2b48b28"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Quadrature rule","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"Hilbert transform","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"Principal value integral","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"Finite-part integral","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"End-point singularities of Jacobi type","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"Chebyshev interpolation","subitem_subject_language":"en","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"journal article","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Algorithms for approximating finite Hilbert transform with end-point singularities and its derivatives","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Algorithms for approximating finite Hilbert transform with end-point singularities and its derivatives","subitem_title_language":"en"}]},"item_type_id":"10001","owner":"18","path":["2404"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2024-02-13"},"publish_date":"2024-02-13","publish_status":"0","recid":"2000117","relation_version_is_last":true,"title":["Algorithms for approximating finite Hilbert transform with end-point singularities and its derivatives"],"weko_creator_id":"18","weko_shared_id":-1},"updated":"2024-02-13T05:12:08.565819+00:00"}