  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.
