We propose a mixed precision Jacobi algorithm for computing the singular value decomposition (SVD) of a dense matrix. After appropriate preconditioning, the proposed algorithm computes the SVD in a lower precision as an initial guess, and then performs one-sided Jacobi rotations in the working precision as iterative refinement. By carefully transforming a lower precision solution to a higher precision one, our algorithm achieves about 2 times speedup on the x86-64 architecture compared to the usual one-sided Jacobi SVD algorithm in LAPACK, without sacrificing the accuracy.

翻译：我们建议使用混合精密的雅各比算法来计算密质矩阵的单值分解(SVD ) 。 在经过适当的先决条件后,提议的算法将SVD以低精度计算为初步猜测,然后在工作精度中进行单向雅各比交替,作为迭接精细化。通过仔细将低精度的解算法转换为更精准的解算法,我们的算法比LAPACK中通常的单向雅各比 SVD 算法加快了2倍左右,同时不牺牲准确性。