{"created":"2021-03-01T06:15:49.274864+00:00","id":9072,"links":{},"metadata":{"_buckets":{"deposit":"9053d012-906b-44a3-8205-a3f634ef3ac3"},"_deposit":{"id":"9072","owners":[],"pid":{"revision_id":0,"type":"depid","value":"9072"},"status":"published"},"_oai":{"id":"oai:nagoya.repo.nii.ac.jp:00009072","sets":["320:321:322"]},"author_link":["25457","25458"],"item_10_alternative_title_19":{"attribute_name":"その他のタイトル","attribute_value_mlt":[{"subitem_alternative_title":"Recent Developments in Algorithms for Solving Dense Eigenproblems (I) : Algorithm of Multiple Relatively Robust Representations","subitem_alternative_title_language":"en"}]},"item_10_biblio_info_6":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2005-06-25","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicPageEnd":"208","bibliographicPageStart":"181","bibliographicVolumeNumber":"15","bibliographic_titles":[{"bibliographic_title":"日本応用数理学会論文誌","bibliographic_titleLang":"ja"}]}]},"item_10_description_4":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"The Algorithm of Multiple Relatively Robust Representations (MR^3) is a new algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem proposed by I.Dhillon in 1997. It has attracted much attention because it can compute all the eigenvectors of an n x n matrix in only O(n^2) work and is easy to parallelize. In this article, we survey the papers related to the MR^3 algorithm and try to present a simple and easily understandable  picture of the algorithm by explaining, one by one, its key ingredients such as the relatively  robust representations of a symmetric tridiagonal matrix, the dqds algorithm for computing accurate eigenvalues and the twisted factorization for computing accurate eigenvectors. Limitations of the algorithm  and directions for future research are also discussed.","subitem_description_language":"en","subitem_description_type":"Abstract"}]},"item_10_identifier_60":{"attribute_name":"URI","attribute_value_mlt":[{"subitem_identifier_type":"HDL","subitem_identifier_uri":"http://hdl.handle.net/2237/10838"}]},"item_10_publisher_32":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"日本応用数理学会","subitem_publisher_language":"ja"}]},"item_10_relation_43":{"attribute_name":"関連情報","attribute_value_mlt":[{"subitem_relation_type":"isVersionOf","subitem_relation_type_id":{"subitem_relation_type_id_text":"http://ci.nii.ac.jp/naid/10016594490/","subitem_relation_type_select":"URI"}}]},"item_10_rights_12":{"attribute_name":"権利","attribute_value_mlt":[{"subitem_rights":"日本応用数理学会","subitem_rights_language":"ja"},{"subitem_rights":"本文データは学協会の許諾に基づきCiNiiから複製したものである","subitem_rights_language":"ja"}]},"item_10_select_15":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_select_item":"publisher"}]},"item_10_source_id_7":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"09172246","subitem_source_identifier_type":"PISSN"}]},"item_10_text_14":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_text_value":"application/pdf"}]},"item_1615787544753":{"attribute_name":"出版タイプ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"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":"山本, 有作","creatorNameLang":"ja"}],"nameIdentifiers":[{"nameIdentifier":"25457","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"Yamamoto, Yusaku","creatorNameLang":"en"}],"nameIdentifiers":[{"nameIdentifier":"25458","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-02-19"}],"displaytype":"detail","filename":"yamamoto_988.pdf","filesize":[{"value":"1.8 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"yamamoto_988.pdf","objectType":"fulltext","url":"https://nagoya.repo.nii.ac.jp/record/9072/files/yamamoto_988.pdf"},"version_id":"3db07cb0-b932-4976-9559-fd379ffdebae"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"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":"密行列固有値解法の最近の発展(I) : Multiple Relatively Robust Representationsアルゴリズム","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"密行列固有値解法の最近の発展(I) : Multiple Relatively Robust Representationsアルゴリズム","subitem_title_language":"ja"}]},"item_type_id":"10","owner":"1","path":["322"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2009-01-21"},"publish_date":"2009-01-21","publish_status":"0","recid":"9072","relation_version_is_last":true,"title":["密行列固有値解法の最近の発展(I) : Multiple Relatively Robust Representationsアルゴリズム"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2023-01-16T03:54:36.310522+00:00"}