{"links":{},"metadata":{"_oai":{"id":"oai:ipsj.ixsq.nii.ac.jp:00219084","sets":["934:1119:10960:10961"]},"path":["10961"],"owner":"44499","recid":"219084","title":["Solving Block Low-Rank Matrix Eigenvalue Problems"],"pubdate":{"attribute_name":"公開日","attribute_value":"2022-07-28"},"_buckets":{"deposit":"bfaff8e7-cb76-4e79-9d5b-8790293e94a6"},"_deposit":{"id":"219084","pid":{"type":"depid","value":"219084","revision_id":0},"owners":[44499],"status":"published","created_by":44499},"item_title":"Solving Block Low-Rank Matrix Eigenvalue Problems","author_link":["571099","571100"],"item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Solving Block Low-Rank Matrix Eigenvalue Problems"},{"subitem_title":"Solving Block Low-Rank Matrix Eigenvalue Problems","subitem_title_language":"en"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"low-rank approximation, block low-rank matrices, hierarchical matrices, eigenvalue problem, block householder transformation, eigensolver","subitem_subject_scheme":"Other"}]},"item_type_id":"3","publish_date":"2022-07-28","item_3_text_3":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Research Institute for Value-Added-Information Generation (VAiG), Japan Agency for Marine-Earth Science and Technology (JAMSTEC)"}]},"item_3_text_4":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_value":"Research Institute for Value-Added-Information Generation (VAiG), Japan Agency for Marine-Earth Science and Technology (JAMSTEC)","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/219084/files/IPSJ-TACS1501005.pdf","label":"IPSJ-TACS1501005.pdf"},"date":[{"dateType":"Available","dateValue":"2024-07-28"}],"format":"application/pdf","billing":["billing_file"],"filename":"IPSJ-TACS1501005.pdf","filesize":[{"value":"2.1 MB"}],"mimetype":"application/pdf","priceinfo":[{"tax":["include_tax"],"price":"0","billingrole":"5"},{"tax":["include_tax"],"price":"0","billingrole":"6"},{"tax":["include_tax"],"price":"0","billingrole":"16"},{"tax":["include_tax"],"price":"0","billingrole":"11"},{"tax":["include_tax"],"price":"0","billingrole":"14"},{"tax":["include_tax"],"price":"0","billingrole":"15"},{"tax":["include_tax"],"price":"0","billingrole":"44"}],"accessrole":"open_date","version_id":"42505573-d055-446a-a2d8-d49c7f6f1a52","displaytype":"detail","licensetype":"license_note","license_note":"Copyright (c) 2022 by the Information Processing Society of Japan"}]},"item_3_creator_5":{"attribute_name":"著者名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Akihiro, Ida"}],"nameIdentifiers":[{}]}]},"item_3_creator_6":{"attribute_name":"著者名(英)","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Akihiro, Ida","creatorNameLang":"en"}],"nameIdentifiers":[{}]}]},"item_3_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA11833852","subitem_source_identifier_type":"NCID"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourceuri":"http://purl.org/coar/resource_type/c_6501","resourcetype":"journal article"}]},"item_3_source_id_11":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"1882-7829","subitem_source_identifier_type":"ISSN"}]},"item_3_description_7":{"attribute_name":"論文抄録","attribute_value_mlt":[{"subitem_description":"To solve large-scale matrix eigenvalue problems (EVPs), a two-step tridiagonalization method using the block Householder transformation (HT) is often employed. Although the method based on dense matrix arithmetic requires a memory storage of O(N2) and an arithmetic operations of O(N3), in this study, these were reduced by approximating the method using block low-rank (BLR-) matrices. A special block HT for BLR-matrices and a two-step tridiagonalization method using it are proposed to solve an EVP with a real symmetric BLR-matrix. In the proposed block HT, block Householder vectors are also formed using BLR-matrices. It is demonstrated how the block size m in the BLR-matrix should be determined and confirmed that the memory and arithmetic complexities of the proposed method were O(N5/3) and O(N7/3), respectively, for typical cases when using an appropriate block size m ∝ N1/3. In numerical experiments of a string free vibration problem with known analytical solutions, for large eigenvalues, the calculated eigenvalues using the proposed method converge toward the analytical ones in accordance with the theoretical convergence curves. Owing to the reduced complexity, an EVP of a matrix was solved with about N = 300,000, which is significantly larger than the limit of the conventional method with dense matrices, within a reasonable amount of time on a CPU core. For the calculation time, the proposed method was faster than the conventional method when the matrix size N was larger than a few tens of thousands.\n------------------------------\nThis is a preprint of an article intended for publication Journal of\nInformation Processing(JIP). This preprint should not be cited. This\narticle should be cited as: Journal of Information Processing Vol.30(2022) (online)\n------------------------------","subitem_description_type":"Other"}]},"item_3_description_8":{"attribute_name":"論文抄録(英)","attribute_value_mlt":[{"subitem_description":"To solve large-scale matrix eigenvalue problems (EVPs), a two-step tridiagonalization method using the block Householder transformation (HT) is often employed. Although the method based on dense matrix arithmetic requires a memory storage of O(N2) and an arithmetic operations of O(N3), in this study, these were reduced by approximating the method using block low-rank (BLR-) matrices. A special block HT for BLR-matrices and a two-step tridiagonalization method using it are proposed to solve an EVP with a real symmetric BLR-matrix. In the proposed block HT, block Householder vectors are also formed using BLR-matrices. It is demonstrated how the block size m in the BLR-matrix should be determined and confirmed that the memory and arithmetic complexities of the proposed method were O(N5/3) and O(N7/3), respectively, for typical cases when using an appropriate block size m ∝ N1/3. In numerical experiments of a string free vibration problem with known analytical solutions, for large eigenvalues, the calculated eigenvalues using the proposed method converge toward the analytical ones in accordance with the theoretical convergence curves. Owing to the reduced complexity, an EVP of a matrix was solved with about N = 300,000, which is significantly larger than the limit of the conventional method with dense matrices, within a reasonable amount of time on a CPU core. For the calculation time, the proposed method was faster than the conventional method when the matrix size N was larger than a few tens of thousands.\n------------------------------\nThis is a preprint of an article intended for publication Journal of\nInformation Processing(JIP). This preprint should not be cited. This\narticle should be cited as: Journal of Information Processing Vol.30(2022) (online)\n------------------------------","subitem_description_type":"Other"}]},"item_3_biblio_info_10":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographic_titles":[{"bibliographic_title":"情報処理学会論文誌コンピューティングシステム（ACS）"}],"bibliographicIssueDates":{"bibliographicIssueDate":"2022-07-28","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"1","bibliographicVolumeNumber":"15"}]},"relation_version_is_last":true,"weko_creator_id":"44499"},"created":"2025-01-19T01:19:25.134604+00:00","updated":"2025-01-19T14:55:50.697348+00:00","id":219084}