{"updated":"2025-01-20T12:50:50.683113+00:00","metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00158496","sets":["1164:2240:8543:8671"]},"path":["8671"],"owner":"11","recid":"158496","title":["Numerical Unstability and Improvement of a No-Pivoting LU Decomposition Algorithm by a Discrete Fourier Matrix"],"pubdate":{"attribute_name":"公開日","attribute_value":"2016-04-18"},"_buckets":{"deposit":"4ac0344b-cd87-452d-8dc4-54fd41bf0fdb"},"_deposit":{"id":"158496","pid":{"type":"depid","value":"158496","revision_id":0},"owners":[11],"status":"published","created_by":11},"item_title":"Numerical Unstability and Improvement of a No-Pivoting LU Decomposition Algorithm by a Discrete Fourier Matrix","author_link":["303367","303368"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Numerical Unstability and Improvement of a No-Pivoting LU Decomposition Algorithm by a Discrete Fourier Matrix"},{"subitem_title":"Numerical Unstability and Improvement of a No-Pivoting LU Decomposition Algorithm by a Discrete Fourier Matrix","subitem_title_language":"en"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"行列計算","subitem_subject_scheme":"Other"}]},"item_type_id":"4","publish_date":"2016-04-18","item_4_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Department of Computer Science, The University of Tokyo"}]},"item_4_text_4":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_value":"Department of Computer Science, The University of Tokyo","subitem_text_language":"en"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_publisher":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"情報処理学会","subitem_publisher_language":"ja"}]},"publish_status":"0","weko_shared_id":-1,"item_file_price":{"attribute_name":"Billing file","attribute_type":"file","attribute_value_mlt":[{"url":{"url":"https://ipsj.ixsq.nii.ac.jp/record/158496/files/IPSJ-HPC16154006.pdf","label":"IPSJ-HPC16154006.pdf"},"date":[{"dateType":"Available","dateValue":"2018-04-18"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-HPC16154006.pdf","filesize":[{"value":"1.1 MB"}],"mimetype":"application/pdf","priceinfo":[{"tax":["include_tax"],"price":"660","billingrole":"5"},{"tax":["include_tax"],"price":"330","billingrole":"6"},{"tax":["include_tax"],"price":"0","billingrole":"14"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_date","version_id":"0bee2c78-6c2d-40ac-90b3-4bc134ee017c","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2016 by the Information Processing Society of Japan"}]},"item_4_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Shohei, Kobayashi"}],"nameIdentifiers":[{}]}]},"item_4_creator_6":{"attribute_name":"著者名(英)","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Shohei, Kobayashi","creatorNameLang":"en"}],"nameIdentifiers":[{}]}]},"item_4_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AN10463942","subitem_source_identifier_type":"NCID"}]},"item_4_textarea_12":{"attribute_name":"Notice","attribute_value_mlt":[{"subitem_textarea_value":"SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc."}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourceuri":"http://purl.org/coar/resource_type/c_18gh","resourcetype":"technical report"}]},"item_4_source_id_11":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"2188-8841","subitem_source_identifier_type":"ISSN"}]},"item_4_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"Linear systems are solved by LU decomposition. Partial pivoting is the most frequently employed way to perform this decomposition. Pivoting is necessary for numerical stability of LU decomposition. However, pivoting is not able to be computed in parallel and pivoting restricts block LU decomposition algorithms. A no-pivoting LU decomposition algorithm has been investigated for more than two decades. This decomposition algorithm without pivoting is efficient for modern computers. However, stabilizing numerical accuracy of solutions of linear systems without pivoting is more difficult than partial pivoting. This thesis researches the algorithm called RDFT that eliminates pivoting nessesity by using random numbers and discrete Fourier transform. We show some examples of LU decomposition by RDFT fail numerically. In addition, we improve the RDFT algorithm with modification to improve numerical stability of such matrices.","subitem_description_type":"Other"}]},"item_4_description_8":{"attribute_name":"論文抄録(英)","attribute_value_mlt":[{"subitem_description":"Linear systems are solved by LU decomposition. Partial pivoting is the most frequently employed way to perform this decomposition. Pivoting is necessary for numerical stability of LU decomposition. However, pivoting is not able to be computed in parallel and pivoting restricts block LU decomposition algorithms. A no-pivoting LU decomposition algorithm has been investigated for more than two decades. This decomposition algorithm without pivoting is efficient for modern computers. However, stabilizing numerical accuracy of solutions of linear systems without pivoting is more difficult than partial pivoting. This thesis researches the algorithm called RDFT that eliminates pivoting nessesity by using random numbers and discrete Fourier transform. We show some examples of LU decomposition by RDFT fail numerically. In addition, we improve the RDFT algorithm with modification to improve numerical stability of such matrices.","subitem_description_type":"Other"}]},"item_4_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicPageEnd":"8","bibliographic_titles":[{"bibliographic_title":"研究報告ハイパフォーマンスコンピューティング（HPC）"}],"bibliographicPageStart":"1","bibliographicIssueDates":{"bibliographicIssueDate":"2016-04-18","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"6","bibliographicVolumeNumber":"2016-HPC-154"}]},"relation_version_is_last":true,"weko_creator_id":"11"},"created":"2025-01-19T00:32:11.265320+00:00","id":158496,"links":{}}