2023-06-10T03:42:51Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:001929562020-10-27T05:02:56Z00934:00989:09407:09598
Improvement of the Augmented Implicitly Restarted Lanczos Bidiagonalization Method in Single Precision Floating Point ArithmeticImprovement of the Augmented Implicitly Restarted Lanczos Bidiagonalization Method in Single Precision Floating Point Arithmeticeng[オリジナル論文] truncated SVD, large-scale sparse matrices, Lanczos algorithm, QR decomposition, Householder reflectorhttp://id.nii.ac.jp/1001/00192867/Articlehttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=192956&item_no=1&attribute_id=1&file_no=1Copyright (c) 2018 by the Information Processing Society of JapanKyoto UniversityNara Women's UniversityKyoto University／Presently with Salesian PolytechnicKyoto UniversityYuya, IshidaMasami, TakataKinji, KimuraYoshimasa, NakamuraEfficient processing for big data is attracting increased attention in many scientific problems. In particular, singular value decomposition (SVD) of matrices is one of the most significant operations in linear algebra. For example, the truncated SVD is used for principal component analysis of large-scale document-term matrices. In this paper, we improve the augmented implicitly restarted Lanczos bidiagonalization (AIRLB) method for the truncated SVD of large-scale sparse matrices. Instead of the conventional method, using the QR decomposition in terms of the Householder reflector, we propose an algorithm that restarts with orthogonalization of both sides of the singular vectors of the small matrix. As a result, in single precision floating point arithmetic, several numerical experiments show that our improvements shorten computation time and increase the accuracy of truncated SVD compared with a conventional algorithm.Efficient processing for big data is attracting increased attention in many scientific problems. In particular, singular value decomposition (SVD) of matrices is one of the most significant operations in linear algebra. For example, the truncated SVD is used for principal component analysis of large-scale document-term matrices. In this paper, we improve the augmented implicitly restarted Lanczos bidiagonalization (AIRLB) method for the truncated SVD of large-scale sparse matrices. Instead of the conventional method, using the QR decomposition in terms of the Householder reflector, we propose an algorithm that restarts with orthogonalization of both sides of the singular vectors of the small matrix. As a result, in single precision floating point arithmetic, several numerical experiments show that our improvements shorten computation time and increase the accuracy of truncated SVD compared with a conventional algorithm.AA11464803情報処理学会論文誌数理モデル化と応用（TOM）11319252018-12-201882-77802018-12-17