M. Takata, K. Kimura, M. Iwasaki, and Y. Nakamura (Japan)
singular value decomposition, high-speed, accuracy, dis crete Lotka-Volterra system, LAPIS, LAPACK
To perform singular value decomposition (SVD) of matri ces with high accuracy and high-speed, we developed a library by using an integrable system called the discrete Lotka-Volterra (dLV) system. The most well-known rou tine for the SVD is DBDSQR provided in LAPACK, which is based on the QRs (QR with shift) algorithm. However, DBDSQR is slow and does not perform well for the case where only a few singular vectors are desirable. Recently a new SVD scheme named Integrable-SVD (I-SVD) was de veloped. The execution time for the I-SVD scheme based on the dLV system and transformation is less. In this pa per, we implement and evaluate the I-SVD scheme. To ex amine its accuracy, we propose a method for making ran dom upper bidiagonal matrices with desired singular val ues. The corresponding singular vectors are also accurately obtained. From the experimental results, we conclude that the singular vectors computed by the I-SVD scheme have adequate orthogonality, and the scheme also has high speed and accuracy for both the computed singular values and vectors.
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