2026-04-16T18:52:40Z https://ipsj.ixsq.nii.ac.jp/oai

oai:ipsj.ixsq.nii.ac.jp:00212232 2025-01-19T17:33:57Z 934:989:10456:10630

On an Implementation of the One-Sided Jacobi Method With High Accuracy On an Implementation of the One-Sided Jacobi Method With High Accuracy Masami, Takata Sho, Araki Takahiro, Miyamae Kinji, Kimura Yoshimasa, Nakamura Masami, Takata Sho, Araki Takahiro, Miyamae Kinji, Kimura Yoshimasa, Nakamura [オリジナル論文] Singular value decomposition, Jacobi method, false-position method, secant method The one-sided Jacobi method for performing singular value decomposition can compute all singular values and singular vectors with high accuracy. Additionally, the computation cost is insignificant for comparatively small matrices. However, in the case of the conventional implementation in Linear Algebra PACKage, the subroutine may not be able to compute a singular vector with sufficient orthogonality. To avoid this problem, we propose a novel implementation of the one-sided Jacobi method. In the proposed implementation, a Givens rotation with high accuracy and fused multiply-accumulate are adopted. The one-sided Jacobi method for performing singular value decomposition can compute all singular values and singular vectors with high accuracy. Additionally, the computation cost is insignificant for comparatively small matrices. However, in the case of the conventional implementation in Linear Algebra PACKage, the subroutine may not be able to compute a singular vector with sufficient orthogonality. To avoid this problem, we propose a novel implementation of the one-sided Jacobi method. In the proposed implementation, a Givens rotation with high accuracy and fused multiply-accumulate are adopted. journal article 情報処理学会 2021-08-10 application/pdf 情報処理学会論文誌数理モデル化と応用（TOM） 3 14 68 75 1882-7780 AA11464803 https://ipsj.ixsq.nii.ac.jp/record/212232/files/IPSJ-TOM1403007.pdf eng