文章基本信息

标题：Error Analysis of the Cholesky QR-Based Block Orthogonalization Process for the One-Sided Block Jacobi SVD Algorithm
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作者：Shuhei Kudo ; Yusaku Yamamoto ; Toshiyuki Imamura 等
期刊名称：COMPUTING AND INFORMATICS
印刷版ISSN：1335-9150
出版年度：2020
卷号：39
期号：6
页码：1203-1228
DOI：10.31577/cai_2020_6_1203
出版社：COMPUTING AND INFORMATICS
摘要：The one-sided block Jacobi method (OSBJ) has attracted attention as a fast and accurate algorithm for the singular value decomposition (SVD). The computational kernel of OSBJ is orthogonalization of a column block pair, which amounts to computing the SVD of this block pair. Hari proposes three methods for this partial SVD, and we found through numerical experiments that the variant named "V2", which is based on the Cholesky QR method, is the fastest variant and achieves satisfactory accuracy. While it is a good news from a practical viewpoint, it seems strange considering the well-known instability of the Cholesky QR method. In this paper, we perform a detailed error analysis of the V2 variant and explain why and when it can be used to compute the partial SVD accurately. Thus, our results provide a theoretical support for using the V2 variant safely in the OSBJ method. Download data is not yet available.
其他摘要：The one-sided block Jacobi method (OSBJ) has attracted attention as a fast and accurate algorithm for the singular value decomposition (SVD). The computational kernel of OSBJ is orthogonalization of a column block pair, which amounts to computing the SVD of this block pair. Hari proposes three methods for this partial SVD, and we found through numerical experiments that the variant named "V2", which is based on the Cholesky QR method, is the fastest variant and achieves satisfactory accuracy. While it is a good news from a practical viewpoint, it seems strange considering the well-known instability of the Cholesky QR method. In this paper, we perform a detailed error analysis of the V2 variant and explain why and when it can be used to compute the partial SVD accurately. Thus, our results provide a theoretical support for using the V2 variant safely in the OSBJ method.
关键词：Singular value decomposition; one-sided Jacobi method; error analysis; parallel computing; orthogonalization Abstract The one-sided block Jacobi method (OSBJ) has attracted attention as a fast and accurate algorithm for the singular value decomposition (SVD);The computational kernel of OSBJ is orthogonalization of a column block pair; which amounts to computing the SVD of this block pair;Hari proposes three methods for this partial SVD; and we found through numerical experiments that the variant named "V2"; which is based on the Cholesky QR method; is the fastest variant and achieves satisfactory accuracy;While it is a good news from a practical viewpoint; it seems strange considering the well-known instability of the Cholesky QR method;In this paper; we perform a detailed error analysis of the V2 variant and explain why and when it can be used to compute the partial SVD accurately;Thus; our results provide a theoretical support for using the V2 variant safely in the OSBJ method;Downloads Download data is not yet available.
其他关键词：Singular value decomposition;one-sided Jacobi method;error analysis;parallel computing;orthogonalization