@article{oai:ipsj.ixsq.nii.ac.jp:02006877,
 author = {Miho,Chiyonobu and Masami,Takata and Kinji,Kimura and Yoshimasa,Nakamura and Miho Chiyonobu and Masami Takata and Kinji Kimura and Yoshimasa Nakamura},
 issue = {1},
 journal = {情報処理学会論文誌数理モデル化と応用（TOM）},
 month = {Jan},
 note = {This study proposes a method for computing partial singular values and the corresponding singular vectors. Principal component analysis (PCA) requires only a few singular values and the corresponding singular vectors. General partial singular value decomposition employs a combination of bisection and inverse iteration methods. However, this method may be unreliable because of the matrices that reduce the calculation accuracy. Consequently, this study employs the orthogonal QD with shift (OQDS) method. The OQDS method can compute singular values from smaller values and the corresponding right-singular vectors with high accuracy to the lower bi-diagonal matrix if the matrix is not split during computation. Under the split, it is unclear which side of the split the smaller singular values fall. Therefore, addressing this split is necessary for adopting the OQDS method for PCA. In this paper, we propose a new implementation of the OQDS method that is unaffected by splits. Our experimental results confirm that this method exhibits fast performance while maintaining reliability., This study proposes a method for computing partial singular values and the corresponding singular vectors. Principal component analysis (PCA) requires only a few singular values and the corresponding singular vectors. General partial singular value decomposition employs a combination of bisection and inverse iteration methods. However, this method may be unreliable because of the matrices that reduce the calculation accuracy. Consequently, this study employs the orthogonal QD with shift (OQDS) method. The OQDS method can compute singular values from smaller values and the corresponding right-singular vectors with high accuracy to the lower bi-diagonal matrix if the matrix is not split during computation. Under the split, it is unclear which side of the split the smaller singular values fall. Therefore, addressing this split is necessary for adopting the OQDS method for PCA. In this paper, we propose a new implementation of the OQDS method that is unaffected by splits. Our experimental results confirm that this method exhibits fast performance while maintaining reliability.},
 pages = {1--13},
 title = {Implementation of the OQDS method with a new shift strategy for Principal Component Analysis},
 volume = {19},
 year = {2026}
}