{"id":208880,"updated":"2025-01-19T18:41:24.775493+00:00","links":{},"created":"2025-01-19T01:10:14.793782+00:00","metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00208880","sets":["1164:2240:10178:10459"]},"path":["10459"],"owner":"44499","recid":"208880","title":["最近点丸めのみを用いた実対称行列に対する標準固有値問題の精度保証法"],"pubdate":{"attribute_name":"公開日","attribute_value":"2020-12-14"},"_buckets":{"deposit":"bdbb09ae-c7f9-4717-b94b-f050dc6acab8"},"_deposit":{"id":"208880","pid":{"type":"depid","value":"208880","revision_id":0},"owners":[44499],"status":"published","created_by":44499},"item_title":"最近点丸めのみを用いた実対称行列に対する標準固有値問題の精度保証法","author_link":["525237","525239","525236","525238"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"最近点丸めのみを用いた実対称行列に対する標準固有値問題の精度保証法"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"数値計算","subitem_subject_scheme":"Other"}]},"item_type_id":"4","publish_date":"2020-12-14","item_4_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"理化学研究所計算科学研究センター"},{"subitem_text_value":"芝浦工業大学システム理工学部数理科学科"},{"subitem_text_value":"東京女子大学現代教養学部数理科学科"},{"subitem_text_value":"理化学研究所計算科学研究センター"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"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/208880/files/IPSJ-HPC20177016.pdf","label":"IPSJ-HPC20177016.pdf"},"date":[{"dateType":"Available","dateValue":"2022-12-14"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-HPC20177016.pdf","filesize":[{"value":"954.7 kB"}],"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":"6fff8a8f-840e-4f07-a3b7-51a01ad58ddc","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2020 by the Information Processing Society of Japan"}]},"item_4_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"寺尾, 剛史"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"尾崎, 克久"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"荻田, 武史"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"今村, 俊幸"}],"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":"実対称行列に対する標準固有値問題の精度保証法は，これまでに様々な手法が提案されてきた．その実装には浮動小数点演算の丸めモードを変更した区間演算がよく用いられるが，この丸めモードの変更は計算機環境によっては難しい場合がある．本発表では，多くの計算機環境でデフォルトで用いられる最近点丸めによる浮動小数点演算のみを用いて，全近似固有値の精度を保証する新しい手法を提案する．また高精度行列積を用いて，大規模行列に対応可能かつ悪条件な行列においても誤差上限の過大評価を抑制する精度保証法を提案する．最後に，速度と精度に対する数値実験を紹介する．提案手法は LAPACK の固有値計算ソルバを用いた全近似固有対の計算時間と比較して，高速な手法の場合は 3 割，高精度な方法の場合 6 割程度の計算時間で誤差上限を計算できた．また，全近似固有値の計算時間と全近似固有対の計算を含む精度保証に要する計算時間は，行列サイズが 20000 の場合に高速な手法は 3.5 倍程度，高精度な手法は 4.5 倍程度で計算できた．また精度に関しては，高速な手法と高精度な手法で誤差の上限を比較し，高精度計算を用いて誤差上限の過大評価を抑制できていることを確認した．","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":"2020-12-14","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"16","bibliographicVolumeNumber":"2020-HPC-177"}]},"relation_version_is_last":true,"weko_creator_id":"44499"}}