{"_buckets": {"deposit": "8e18af74-8cdf-4ccc-8c58-0027ec2495aa"}, "_deposit": {"id": "394", "owners": [], "pid": {"revision_id": 0, "type": "depid", "value": "394"}, "status": "published"}, "_oai": {"id": "oai:repository.nii.ac.jp:00000394", "sets": ["136"]}, "author_link": [], "control_number": "394", "item_5_biblio_info_30": {"attribute_name": "書誌情報", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "2004-05-07", "bibliographicIssueDateType": "Issued"}, "bibliographicPageEnd": "29", "bibliographicPageStart": "1", "bibliographic_titles": [{"bibliographic_title": "NIIテクニカル・レポート", "bibliographic_titleLang": "ja"}, {"bibliographic_title": "NII Technical Report", "bibliographic_titleLang": "en"}]}]}, "item_5_description_28": {"attribute_name": "抄録", "attribute_value_mlt": [{"subitem_description": "For least squares problems of minimizing || b - A x ||_2 where A is a large sparse m x n (m \u003e= n) matrix, the common method is to apply the conjugate gradient method to the normal equation A^T A x = A^T b. However, the condition number of A^T A is square of that of A, and convergence becomes problematic for severely ill-conditioned problems even with preconditioning. In this paper, we propose two methods for applying the GMRES method to the least squares problem by using a n x m matrix B. We give the necessary and sufficient condition that B should satisfy in order that the proposed methods give a least squares solution. Then, for implementations for B, we propose an incomplete QR decomposition IMGS(l). Numerical experiments show that the simplest case l=0, which is equivalent to B= ( diag (A^T A) )^(-1) A^T, gives best results, and converges faster than previous methods for severely ill-conditioned problems.", "subitem_description_language": "en", "subitem_description_type": "Abstract"}]}, "item_5_identifier_registration": {"attribute_name": "ID登録", "attribute_value_mlt": [{"subitem_identifier_reg_text": "10.20736/0000000394", "subitem_identifier_reg_type": "JaLC"}]}, "item_5_publisher_31": {"attribute_name": "出版者", "attribute_value_mlt": [{"subitem_publisher": "国立情報学研究所", "subitem_publisher_language": "ja"}]}, "item_5_source_id_32": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "1346-5597", "subitem_source_identifier_type": "ISSN"}]}, "item_creator": {"attribute_name": "著者", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "伊藤, 徳史", "creatorNameLang": "ja"}, {"creatorName": "Ito, Tokushi", "creatorNameLang": "en"}]}, {"creatorNames": [{"creatorName": "速水, 謙", "creatorNameLang": "ja"}, {"creatorName": "Hayami, Ken", "creatorNameLang": "en"}]}]}, "item_files": {"attribute_name": "ファイル情報", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2015-08-27"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "04-006E.pdf", "filesize": [{"value": "363.7 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 363700.0, "url": {"label": "NII Technical Report (NII-2004-006E)：Preconditioned GMRES Methods for Least Squares Problems", "url": "https://repository.nii.ac.jp/record/394/files/04-006E.pdf"}, "version_id": "43aa6a1e-fd58-432a-911c-eb721781dcfa"}]}, "item_keyword": {"attribute_name": "キーワード", "attribute_value_mlt": [{"subitem_subject": "テクニカルレポート", "subitem_subject_language": "ja", "subitem_subject_scheme": "Other"}, {"subitem_subject": "Technical Report", "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": "departmental bulletin paper", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "NII Technical Report (NII-2004-006E)：Preconditioned GMRES Methods for Least Squares Problems", "item_titles": {"attribute_name": "タイトル", "attribute_value_mlt": [{"subitem_title": "NII Technical Report (NII-2004-006E)：Preconditioned GMRES Methods for Least Squares Problems", "subitem_title_language": "en"}]}, "item_type_id": "5", "owner": "1", "path": ["136"], "permalink_uri": "https://doi.org/10.20736/0000000394", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2004-05-07"}, "publish_date": "2004-05-07", "publish_status": "0", "recid": "394", "relation": {}, "relation_version_is_last": true, "title": ["NII Technical Report (NII-2004-006E)：Preconditioned GMRES Methods for Least Squares Problems"], "weko_shared_id": -1}